Program to find nth term of given Geometric Progression

Given three integers the first term a, common ratio r, and position n, find the n-th term of a geometric progression.
Note: Since the result can be large, return the answer modulo 10⁹ + 7.

Examples:

Input: a = 2, r = 2, n = 4
Output: 16
Explanation: The GP series is 2, 4, 8, 16, ... The 4th term is 16.

Input: a = 4, r = 3, n=3
Output: 36
Explanation: The GP series is 4, 12, 36, 108,.. in which 36 is the 3rd term.

Approach 1: Using a Loop (Naive)

The n-th term can be computed manually by repeatedly multiplying the first term by the common ratio r, a total of n − 1 times.

16

Approach 2: Using Binary Exponentiation (Efficient)

The n-th term of a geometric progression, Tn = a × r^(n−1), can be found by raising the common ratio to the power (n−1). Instead of multiplying repeatedly, binary exponentiation smartly breaks the power into smaller parts using squaring, making the process much faster and efficient.

16