Sum Of Terms In  An Arithmetic Progression

Introduction

Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms remains constant. One common task in AP is finding the sum of terms, which allows us to determine the total value of all terms in the sequence up to a certain position. In this article, we will explore an iterative approach to finding the sum of terms in an Arithmetic Progression. We will discuss the understanding, approach, step-by-step solution, and provide sample code to illustrate the process.

Understanding Arithmetic Progression

Arithmetic Progression is a sequence of numbers in which the difference between consecutive terms, known as the common difference, remains constant. Each term can be obtained by adding the common difference to the previous term. The sum of terms represents the total value of all terms in the sequence up to a certain position.

Approach

To find the sum of terms in an Arithmetic Progression using iteration, we can start with the first term and repeatedly add the terms up to the desired position.

Step-by-Step Solution

1. Input the first term (a), the common difference (d), and the position of the last term (N) for which we want to find the sum.

2. Initialize a variable (sum) to store the sum of terms. Set it equal to the first term (a).

3. Initialize a variable (currentTerm) to store the current term. Set it equal to the first term (a).

4. Iterate from 2 to N: a. Add the common difference (d) to the current term (currentTerm). b. Add the current term to the sum of terms (sum).

5. After the loop, the sum will hold the total value of all terms in the Arithmetic Progression up to the position N.

6. Output the sum of terms.

Code

Here's an example implementation: