Nth Term In A Geometric Progression

Introduction

Geometric Progression (GP) is a sequence of numbers in which each term is obtained by multiplying the previous term by a constant ratio. In this article, we will discuss an iterative approach to finding the Nth term in a Geometric Progression. We will cover the understanding of Geometric Progression, the approach to finding the Nth term, and provide a step-by-step solution with sample code.

Understanding Geometric Progression

A Geometric Progression is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed ratio called the common ratio (r). The general form of a Geometric Progression is a, ar, ar^2, ar^3, ..., where 'a' is the first term and 'r' is the common ratio.

Approach

To find the Nth term in a Geometric Progression, we can use an iterative approach. Starting from the first term (a), we can multiply the term by the common ratio (r) N-1 times to obtain the Nth term. By iteratively applying the common ratio, we can calculate the desired term efficiently.

Step-by-Step Solution

1. Input the values of the first term 'a', the common ratio 'r', and the value of N representing the term we want to find.

2. Initialize a variable 'currentTerm' with the value of the first term 'a'.

3. Iterate N-1 times: a. Multiply the 'currentTerm' by the common ratio 'r'. b. Update the value of 'currentTerm' with the result of the multiplication.

4. The value of 'currentTerm' after the loop will be the Nth term in the Geometric Progression.

Code

Here's an example implementation for finding the Nth term in a Geometric Progression using iteration: