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Arithmetic Progression Formula: Key Concepts, Examples, and Use Cases

Arithmetic Progression Formula: Key Concepts, Examples, and Use Cases

Q: 1. How to find the nth term of arithmetic progression?

Use the formula an=a1+(n-1)×d, where a is the first term and d is the common difference.

Q: 2. Is 2, 2, 2, 2 an arithmetic progression?

Yes, because the common difference (d) is 0 between consecutive terms.

Q: 3. What is the difference between AP and GP?

In AP, the difference between consecutive terms is constant, while in GP, the ratio between consecutive terms is constant.

Q: 4. What is the formula of sum in arithmetic progression?

The sum is Sn= n2×(2a1+(n-1)×d) or Sn= n2×(a1+l)

Q: 5. What is n in arithmetic progression?

The term n represents the total number of terms in the sequence.

Q: 6. What is Sn in arithmetic progression?

Sn is the sum of the first n terms of the arithmetic progression.

Q: 7. Is the nth term the last term in arithmetic progression?

Yes, the nth term is the last if the sequence has n terms.

Q: 8. How to find arithmetic mean?

The arithmetic mean is the average of two terms: AM = Sum of termsNumber of terms

Q: 9. What is the sum of n odd numbers?

The sum of n odd numbers is n2, where n is the count of odd numbers.

Q: 10. What is the sum of first n natural numbers?

The sum of the first n natural number is calculated using Sn=n(n+1)2

By Pavan Vadapalli

Updated on Feb 05, 2025 | 18 min read | 7.7k views

Table of Contents

Arithmetic progression is a number sequence that follows a consistent pattern where the difference between consecutive terms is constant. This feature makes it a predictive series, allowing you to determine the next term or any term at a given position.

This blog covers arithmetic progression, practical applications and practice problems to increase your understanding. Dive in!

What is Arithmetic Progression? Notations and Types

An Arithmetic Progression (AP) is a number sequence where the difference between any two consecutive numbers remains constant. This constant difference called the common difference, defines the progression.

For example, consider a number sequence 3, 6, 9, 12, 15.

In this sequence, the difference between consecutive terms is always 3, making it an arithmetic progression.

Arithmetic progression is a fundamental concept in statistics, used to model linear trends and averages. It is also used in other real-world applications, such as physics, finance, and even everyday problem-solving.

Learn how mathematical concepts can help you master software development fundamentals. Enrol in upGrad’s Online Software Development Courses and grow your knowledge of these core techniques.

Arithmetic progression is calculated using a mathematical formula, which is discussed in the following section.

Notation in Arithmetic Progression Formula

In arithmetic progression, specific notations and formulas are used to describe the sequence and calculate its properties efficiently. These include:

First term (a₁): The initial term of the sequence.
Common difference (d): The constant value added to each term to get the next.
Nth term (aₙ): The term at a specific position in the sequence.
Sum of the first n terms (Sₙ): The sum of all terms up to the nth position

Let’s explore the different notations in the subsequent section.

First Term (a₁)

The first term (a₁) is the starting value of the sequence and forms the basis for calculating all other terms.

For example, consider a sequence 2, 5, 8, 11. The first term (a₁) is 2

Common Difference (d)

The common difference (d) is the constant value added to each term to get the next one. It is calculated using the formula,

d = a_{n} - a_{n - 1}

For example, consider a sequence 2, 4, 6, 8,

Here, d = 4 − 2 = 2

Nth Term (an)

The nth term represents the value of the sequence at the nth position. It is calculated using the following formula.

a_{n} = a_{1} + (n - 1) \times d

Where,

a_n= nth term of the sequence

a₁= first term of the sequence

n = position of the term in the sequence

d = common difference between consecutive terms

Example: For the sequence 5, 10, 15, to find the 5th term.

a₅= 5 + (5 - 1) 5

The 5th term is 25

Sum of the first n terms

The sum of the first n terms is the cumulative total of the sequence up to the n-th term. The formula is:

S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) \times d)

It can be alternatively written as:

S_{n} = \frac{n}{2} (a_{1} + a_{n})

Example: For the sequence 3, 6, 9, 12, the sum of the first 4 terms is:

S_{4} = \frac{4}{2} (3 + 12)

The sum of the first 4 terms is 30.

Now that you’ve explored the different annotations used in the arithmetic progression (AP) formula, let’s check out the different types of AP series formulas.

Types of Arithmetic Progression

Arithmetic Progression (AP) can be classified based on the nature of the sequence. These types will help you understand how AP functions across different conditions.

Here are the different types of arithmetic progression formulas.

1. Finite AP

A finite AP has a specific number of terms and ends after the last term. It is commonly used in practical applications where data has a fixed range.

Example: The provided sequence 2, 4, 6, 8, 10 is a finite AP with 5 terms and a common difference of 2.

2. Infinite AP

An infinite AP continues indefinitely without any end. It is usually theoretical and used in mathematical studies and derivations.

Example: The given sequence 5, 10, 15, 20, ... is an infinite AP with a common difference of 5.

3. Special Cases

There are two types of special cases: AP with a constant common difference and AP with a systematic increase or decrease.

AP with a Constant Common Difference: In this sequence, all terms in the sequence increase or decrease by the same value.

Example: For the sequence 3, 6, 9, 12, the common difference is consistently 3.

AP with Systematic Increase or Decrease: In this sequence, the terms systematically grow larger (positive d) or smaller (negative d).

Example: Used in inflation modeling to predict the rise in prices of goods or services over a fixed period with a constant annual increase.

Example: Depreciation in accounting to calculate the decreasing value of an asset over time with a fixed yearly reduction.

Now that you know the different types of arithmetic progressions, let’s understand their applications in the real world.

Use of Arithmetic Progression Formula

The arithmetic progression formula has practical applications in various fields, starting from finance to theoretical physics.

Here are the different applications of the arithmetic progression formula in the real world.

EMI Calculations in Finance

EMI usually involves uniform monthly reductions in the principal balance, which can be modeled as an AP. The sum of installments is calculated using the formula for the sum of n terms.

Savings Plans and Loan Payments

Using Excel formulas, you calculate the sum of an arithmetic progression or predict future values in savings or loan plans.

Motion Calculation in Physics

Uniform acceleration or deceleration creates velocities that form an AP. For instance, if a vehicle accelerates at a constant rate, its speed readings at equal time intervals follow an arithmetic progression.

Computer Algorithms

AP series formula is used to design algorithms for evenly distributing tasks, such as managing memory allocation. In machine learning and deep learning, AP concepts are integral in designing algorithms and managing sequential data efficiently.

Also Read: A Guide to the Types of AI Algorithms and Their Applications

Studying Population Growth

Predicting population growth or decline over the years under constant growth rates can be represented as an AP. Data analytics professionals use AP series formulas to model population trends and project linear growth in datasets.

Design and Architecture

While designing staircases, the heights of steps often follow an arithmetic progression to ensure uniformity and ease of climbing.

To solve real-world problems using arithmetic progressions, it's essential to have a detailed understanding of the AP series formula. Let’s check out how to apply it in the following section.

Understanding and Applying the Arithmetic Progression Formula

Arithmetic progression (AP) formulas allow you to solve problems that involve sequences. The formula can be varied to find specific terms in a sequence or calculate the sum of multiple terms.

Here are the different forms of AP series formulas and how to use them to solve problems.

General Form of AP

In general, the arithmetic progression can be represented as,

a_{n} = a_{1}, a_{1} + d, a_{1} + 2 d, . . . ., a_{1} + (n - 1) d

Where,

a₁ is the 1st term

d is the common difference

n is the position of the term

Example: Consider a sequence 3, 8, 13, 18…. Where we have to find the 6th term. Based on the sequence, you can deduce that 1st term (a₁) is 3 and the difference (d) is 5.

The 6th term (a₆) is calculated as:

a_{6} = a_{1} + (n - 1) d \Rightarrow a_{6} = 3 + (6 - 1) 5 \Rightarrow a_{6} = 3 + 25 = 28

The Nth term of AP

The nth term in an arithmetic progression is calculated using the following formula.

a_{n} = a_{1} + (n - 1) \times d

Where,

a_n is the nth term in the sequence

a₁ is the 1st term in the sequence

n is the position of the nth term

d is the difference in the sequence

Example: Consider an arithmetic progression 2, 4, 6, 8,… where you have to find the 10th term in the sequence.

Using the formula mentioned above, we get the following equation.

a_{10} = 2 + (10 - 1) 2

Where,

a₁₀ represents the 10th term

2 is the 1st term in the sequence

10 is the position of the 10th term

2 is the difference between the terms

a_{10} = 2 + 18 = 20

Sum of n terms in AP

The sum of the first n terms of an AP can be calculated if the first term, common difference and the total terms are known. The formula for calculation is:

S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) \times d)

Where,

S_n is the sum of the first n terms in the AP

a₁is the first term of the sequence

n is the number of terms to be summed

d is the common difference between consecutive terms

Example: Consider an AP 1, 3, 5, 7, 9 where you need to calculate the sum of the first 5 terms.

In this sequence, you can deduce that a1 is 1, n (number of terms) is 5, and d (difference) is 2.

Inserting these values in the formula, you get.

S_{5} = \frac{5}{2} (2 \cdot 1 + (5 - 1) \times 2) = \frac{5}{2} (10) = 25 \Rightarrow S_{5} = 25

Also Read: Python Program for Sum of Digits

Sum of all terms in a finite AP with the last terms as "l"

You can calculate the sum of an arithmetic progression of the last term, l, is given. The formula is given as:

S_{n} = \frac{n}{2} (a + l)

Where,

S_n is the sum of the first n terms in the AP

a₁is the first term of the sequence

n is the number of terms to be summed

l is the last term of the sequence

Example: Consider an AP sequence 2, 4, 6, 8, 10 where you have to calculate the sum of all the terms. The last term l (10 ) is given.

In this sequence, you can deduce that a1 is 2, n (number of terms) is 5, and l (last term) is 10. Inserting these values in the formula, you get:

S_{5} = \frac{5}{2} (2 + 10) = 30 \Rightarrow S_{5} = 30

Now that you’ve learned about the various arithmetic progression formulas, let’s take a closer look at the formula used to calculate the sum of an arithmetic progression.

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Understanding the Sum Formula for Arithmetic Progression

The sum formula can calculate the total of a sequence of terms where the difference between consecutive terms remains constant. It can be solved if the first term, common difference and the total terms are known. The formula for calculation is:

S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) \times d)

Where,

S_n is the sum of the first n terms in the AP

a₁is the first term of the sequence

n is the number of terms to be summed

d is the common difference between consecutive terms

Here’s a step-by-step derivation of this formula.

Step 1: The sum of the first n terms (S_n) of an AP is the sum of the sequence:

S n = a_{1} + (a_{1} + d) + (a_{1} + 2 d) + . . . . + [a_{1} + (n - 1) d]

Step 2: Write the same sequence in reverse order:

S n = a_{1} + [a_{1} + (n - 1) d] + [a_{1} + (n - 2) d] + . . . . + a_{1}

Step 3: Add the Two Equations

S n + S n = a_{1} + [a_{1} + (n - 1) d] + (a_{1} + d) + [a_{1} + (n - 2) d] + . . . .

Here, each pair in the term equals, 2a₁+(n-1) d

Since there are n such pairs,

2 S n = n \times (2 a_{1} + (n - 1) d)

Step 4: Divide both sides by 2 to isolate Sn

S n = \frac{n}{2} \times (2 a_{1} + (n - 1) d)

For greater understanding, you can write this formula as:

S n = \frac{n}{2} \times (2 a_{1} + (n - 1) d)

Now, let’s consider an example and solve the problem in a step-by-step manner for easy understanding.

Example: Find the sum of the first 6 terms of the AP: 3, 7, 11, 15, . . .

Solution: Here are the steps to solve the problem.

Step 1: The first step in solving the problem is identifying the given values to substitute into the formula. Let’s write the formula and identify terms.

S n = \frac{n}{2} \times (2 a_{1} + (n - 1) d)

Here,

n (number of terms) is 6

a₁(1st term) is 3

d (difference between terms) is 4

Step 2: Substitute the values in the formula. You’ll get the following equation.

S_{6} = \frac{6}{2} \times (2 \times 3 + (6 - 1) \times 4) = 3 \times (6 + (5) \times 4) = 3 \times (6 + 20) = 78 \Rightarrow S_{6} = 78

Thus, the sum of the first 6 terms of the given AP is 78.

The arithmetic progression sum formula has applications in sectors such as salary calculation, loan payments, and population growth. Here are some of its applications.

Salary Increments

Annual salary increments that grow by a fixed amount over time form an AP. The sum formula can be used to calculate the total earnings over a specific period.

Savings Plans

Regular savings with a fixed monthly increment can be considered as an AP. The sum formula calculated the total amount saved after a specific number of months.

Loan Payments

Fixed loan payments with a gradual reduction in interest portions can form an AP. The sum formula can calculate the total payments over the loan term.

Population Growth

In certain cases, population growth models consider a fixed yearly increase (linear growth). The sum formula is applied to calculate the total population over time, especially in short-term predictions.

Now that you’ve learned how to apply the sum formula and explored its practical applications, let’s apply our knowledge to solve some problems related to arithmetic progression.

Solving Arithmetic Progression Problems

Arithmetic progression problems can be solved using the formulas discussed in the previous sections. You can also implement these problems using programming languages like C, Java, Python, C++, JavaScript, or PHP.

Here are some examples of the implementation of arithmetic progression.

Example 1

Problem: Find the general term for the arithmetic progression

- 3, - (\frac{1}{2}), 2, . . .

Solution: You can solve this problem using the formula:

a_{n} = a_{1} + (n - 1) d

Here,

a₁(1st term) is -3
d (difference) is calculated using

a_{2} - a_{1} = - (\frac{1}{2}) - (- 3) = \frac{5}{2}

Substituting this value, you get:

a_{n} = - 3 + (n - 1) \frac{5}{2} = - 3 + \frac{5}{2} n - \frac{5}{2} = \frac{5}{2} n - \frac{11}{2} \Rightarrow a_{n} = \frac{5}{2} n - \frac{11}{2}

This is the general formula for finding the position of any term in the given AP.

Example 2

Problem: Determine which term of the arithmetic progression 3, 8, 13, 18,… is equal to 78.

Solution: You can solve this problem using the following AP series formula:

a_{n} = a_{1} + (n - 1) d

In this problem, an is given as 78. You need to calculate its position, which is n.

For this problem, a₁= 3, d = 5, and an = 78. Inserting these values in the formula, you get.

78 = 3 + (n - 1) 5 \Rightarrow 78 = 3 + 5 n - 5 \Rightarrow 78 = 5 n - 2 \Rightarrow 80 = 5 n \Rightarrow n = 16

Thus, the term 78 appears at the 16th position in the given AP.

Example 3

Problem: Find the sum of the first 5 terms of the arithmetic progression with a first term of 3 and a fifth term of 11.

Solution: You can solve this problem using the sum formula, which is:

S n = \frac{n}{2} \times (2 a_{1} + (n - 1) d)

Based on the problem statement, a₁= 3, a_n= 11, and n = 5. You need to calculate d to solve the equation.

d is calculated using the following AP series formula:

a_{n} = a_{1} + (n - 1) d \Rightarrow 11 = 3 + (5 - 1) d \Rightarrow 11 = 3 + (4 d) \Rightarrow 4 d = 8 \Rightarrow d = 2

Now, inserting values in the sum equation, you get:

S_{5} = \frac{5}{2} \times (2 \times 3 + (5 - 1) \times 2) = \frac{5}{2} \times (14) = 35 \Rightarrow S_{5} = 35

Thus, the sum of the first 5 terms of the given arithmetic progression is 35.

Now that you’ve solved examples of arithmetic progression and implemented them in Python, let’s explore some practice questions to deepen your understanding of the topic.

Arithmetic Progression Formula: Basic to Advanced Problems

For solving arithmetic progression problems, you need to recognize patterns, identify the common differences, and apply formulas to find specific terms or sums.

Here are some practice problems that will cover different types of arithmetic progression formulas.

General Form of AP

To solve problems on the general form of arithmetic progression, you need to use the following formula.

a_{n} = a_{1} + (n - 1) d

Here are some of the practice questions on this AP series formula.

1. Write the general form of the AP where the first term is 7 and the common difference is 5.

Solution: In this problem, a1 is given as 7 and d is given as 5. Using this information, you have to form a general equation to find the location of any term in the given AP.

Inserting the values in the general formula, you get:

a_{n} = 7 + (n - 1) \times 5 = 5 n + 2 \Rightarrow a_{n} = 5 n + 2

Thus, the general term is, a_n=5_n+2

2. If an AP starts with 3 and the common difference is 2, write the first five

terms of the sequence.

Solution: In this problem, a₁ is given as 3, d is given as 2 and n is the position of the term.

Using these values in the general formula, you get:

a_{1} = 3 + (1 - 1) \times 2 = 3 a_{2} = 3 + (2 - 1) \times 2 = 5 a_{3} = 3 + (3 - 1) \times 2 = 7 a_{4} = 3 + (4 - 1) \times 2 = 9 a_{5} = 3 + (5 - 1) \times 2 = 11

Thus, the first 5 terms of the AP are 3, 5, 7, 9, and 11.

Now that you’ve solved some questions on the general AP series formula, let’s solve some on the nth term of AP.

The Nth Term of an AP

To solve problems on nth term of an AP, you need to use the same general formula, which is:

a_{n} = a_{1} + (n - 1) d

Here are some practice questions based on this concept.

1. Find the 12th term of the AP where a₁= 4 and d = 3.

Solution: To solve this problem, insert these values in the general formula. You will get the following equation. Here, n is 12.

a_{12} = 4 + (12 - 1) \times 3 = 37 \Rightarrow a_{12} = 37

Thus, the 12th term in the given AP is 37.

2. If a₁ = 10 and d = 7, what is the 20th term of the AP?

Solution: In this problem, a₁ is given as 10, d as 7, and n as 20. Inserting these values in the above formula, you get the following equation.

a_{20} = 10 + (20 - 1) \times 7 = 143 \Rightarrow a_{20} = 143

Thus, the 20th term in the given AP is 143.

Now that you’ve tackled problems on nth term in an AP, let’s move on to solving problems related to the sum of n terms using the sum formula.

Sum of n Terms in an AP

The sum of n terms is calculated using the following AP series formula.

S n = \frac{n}{2} \times (2 a_{1} + (n - 1) d)

Here are some practice questions on this arithmetic progression formula.

1. Calculate the sum of the first 15 terms of an AP where a₁ = 6 and d = 4.

Solution: In this problem, a₁ is given as 6, d is 4, and n is given as 15. Inserting these values in the sum formula, you get:

S_{15} = \frac{15}{2} \times (2 \times 6 + (15 - 1) \times 4) = \frac{15}{2} \times (12 + 56) = 510 \Rightarrow S_{15} = 510

Thus, the sum of the first 15 terms of the AP is 510.

2. If the sum of the first 10 terms of an AP is 240 and the common

the difference is 5, find the first term.

Solution: In this given problem, S_n is 240, n is 10, and d is 5. You need to calculate the first term, which is a₁.

Inserting these values in the sum formula, you get the following equation.

240 = \frac{10}{2} \times (2 \times a_{1} + (10 - 1) \times 5) = 10 a_{1} + 225 \Rightarrow 240 = 10 a_{1} + 225 \Rightarrow 10 a_{1} = 240 - 225 \Rightarrow 10 a_{1} = 15 \Rightarrow a_{1} = 1.5

Thus, the first term in the given AP is 1.5.

Now that you’ve solved problems on the sum formula, let’s move to problems based on finite AP.

Sum of All Terms in a Finite AP with Last Term (l)

If the last term (l) is known, the sum of all terms in an AP is calculated using the following formula.

math xmlns="http://www.w3.org/1998/Math/MathML"> Sn = n 2 ( a 1 + l )

Here are some practice questions based on this arithmetic progression formula.

1. Find the sum of an AP where a₁= 8, l = 50, and n = 10.

Solution: In this problem, you have to calculate S10using the formula given above. Inserting these values, you get:

S_{10} = \frac{10}{2} \times (8 + 50) S_{10} = \frac{10}{2} \times (58) S_{10} = 290

Thus, the sum of the first 10 terms in the given AP is 290.

2. If the first term of an AP is 2, the last term is 100, and there are 20 terms, calculate the total sum.

Solution: Here, a₁ is 2, l is 100, and n is 20. You need to calculate S₂₀. Inserting these values in the above formula, you get.

S_{20} = \frac{20}{2} \times (2 + 100) S_{20} = \frac{20}{2} \times (102) S_{20} = 1020

Thus, the sum of the first 20 terms in the AP is 1020.

Now that you’ve solved questions based on the arithmetic progression formula, you can test your knowledge by solving these practice questions.

Practice Problem - Top Questions on Arithmetic Progressions

Practicing problems on arithmetic progressions will help you develop a strong foundation in understanding and applying this topic and using it to solve real-world problems.

Here are some arithmetic progression practice questions in the form of MCQs and descriptive questions.

Simple Multiple Choice Questions

Basic multiple-choice questions focus on simple calculations and foundational knowledge essential for understanding arithmetic progression.

Here are some questions for your practice.

1. What is the common difference of the arithmetic progression 2, 5, 8, 11,…?

A) 2

B) 3

C) 5

D) 6

2. Find the 10th term of the AP 3, 7, 11, 15,…?

A) 43

B) 40

C) 39

D) 37

3. Which of the following sequences is not an AP?

A) 1, 2, 3, 4, 5

B) 3, 6, 9, 12

C) 2, 5, 10, 17

D) 4, 7, 10, 13

4. The sum of the first 5 terms of the AP 6, 11, 16, 21,…is:

A) 50

B) 85

C) 65

D) 75

5. If the 4th term of an AP is 15 and the common difference is 3, what is the first term?

A) 3

B) 6

C) 9

D) 12

6. Which formula is used to find the nth term of an AP?

A) a_{n} = a_{1} + (n - 1) \times d B) a_{n} = a_{1} (n) \times d C) a_{n} = a_{1} - (n - 1) \times d D) a_{n} = a_{1} \times (n - 1) \times d

7. If the sum of the first n terms of an AP is given by

S_{n} = 3 n^{2} + 2 n

what is the first term?

A) 2

B) 3

C) 5

D) 7

8. Find the common difference of the AP if the 3rd term is 14 and the 7th term is 26.

A) 4

B) 3

C) 2

D) 5

9. Which of the following represents the sum of the first n terms of an AP?

S_{n} = \frac{n}{2} \times (2 a_{1} + (n - 1) \times d)

S_{n} = \frac{n}{2} \times (a_{1} + l)

C) Both A and B

D) None of the above

10. In an AP, if the first term is 7 and the 5th term is 31, what is the common difference?

A) 8

B) 6

C) 10

D) 9

Now that you’ve seen the multiple-choice questions on arithmetic progression, let’s explore some descriptive questions.

Descriptive Questions

The descriptive questions will test your deeper understanding of arithmetic progression by focusing on detailed explanations, derivations, and problem-solving steps.

Here are some descriptive questions on arithmetic progression.

1. Find the sum of the first 20 terms of the AP 4, 8, 12, 16,. . .

2. If the 8th term of an AP is 52 and the common difference is 7, find the first

Term.

3. Determine the number of terms in the AP 2, 4, 6,…,200.

4. The sum of the first n terms of an AP is 5n²+2n. Find the common difference.

5. Prove that the sum of the first n terms of an AP is

S_{n} = \frac{n}{2} \times (2 a_{1} + (n - 1) \times d)

6. Find the nth term of the AP whose first term is 9 and the common difference

is 4.

7. The 15th term of an AP is 62. If the first term is 7, find the common difference.

8. Three terms, a − d, a, a + d, form an AP. Prove that their sum is 3a.

9. In an AP, the sum of the first 10 terms is 220, and the 10th term is 55. Find the

first term.

10. If the first term of an AP is 12 and the last term is 84, with a common difference

of 6, find the total number of terms in the AP.

Now that you’ve explored some practice questions to strengthen your knowledge of arithmetic progression, let’s understand how you can master this concept for your future career.

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Frequently Asked Questions (FAQs)

1. How to find the nth term of arithmetic progression?

2. Is 2, 2, 2, 2 an arithmetic progression?

3. What is the difference between AP and GP?

4. What is the formula of sum in arithmetic progression?

5. What is n in arithmetic progression?

6. What is Sn in arithmetic progression?

7. Is the nth term the last term in arithmetic progression?

8. How to find arithmetic mean?

9. What is the sum of n odd numbers?

10. What is the sum of first n natural numbers?

11. What is the nth term from last in arithmetic progression?

Pavan Vadapalli

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Arithmetic Progression Formula: Key Concepts, Examples, and Use Cases

What is Arithmetic Progression? Notations and Types

Notation in Arithmetic Progression Formula

First Term (a1)

Common Difference (d)

Nth Term (an)

Sum of the first n terms

Types of Arithmetic Progression

Use of Arithmetic Progression Formula

Understanding and Applying the Arithmetic Progression Formula

General Form of AP

The Nth term of AP

Sum of n terms in AP

Sum of all terms in a finite AP with the last terms as "l"

Understanding the Sum Formula for Arithmetic Progression

Solving Arithmetic Progression Problems

Example 1

Example 2

Example 3

Arithmetic Progression Formula: Basic to Advanced Problems

General Form of AP

The Nth Term of an AP

Sum of n Terms in an AP

Sum of All Terms in a Finite AP with Last Term (l)

Practice Problem - Top Questions on Arithmetic Progressions

Simple Multiple Choice Questions

Descriptive Questions

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Frequently Asked Questions (FAQs)

1. How to find the nth term of arithmetic progression?

2. Is 2, 2, 2, 2 an arithmetic progression?

3. What is the difference between AP and GP?

4. What is the formula of sum in arithmetic progression?

5. What is n in arithmetic progression?

6. What is Sn in arithmetic progression?

7. Is the nth term the last term in arithmetic progression?

8. How to find arithmetic mean?

9. What is the sum of n odd numbers?

10. What is the sum of first n natural numbers?

11. What is the nth term from last in arithmetic progression?

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First Term (a₁)