Find Nth term of the series 5, 10, 20, 40...

Given a positive integer N, the task is to find the Nth term of the series

5, 10, 20, 40....till N terms

Examples:

Input: N = 5
Output: 80

Input: N = 3
Output: 20

Approach: 

1st term = 5 * (2 ^ (1 - 1))  = 5

2nd term = 5 * (2 ^ (2 - 1)) = 10

3rd term = 5 * (2 ^ (3 - 1)) = 20

4th term = 5 * (2 ^ (4 - 1)) = 40

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Nth term = 5 * (2 ^ (N - 1))

The Nth term of the given series can be generalized as-

T_N = (a * (r ^ (N - 1))

The following steps can be followed to derive the formula-

The series 5, 10, 20, 40....till N terms 

is in G.P. with 

first term a = 5

common ratio r = 2 because each term is double the one before it.

The Nth term of a G.P. is

T_N = (a * (r ^ (N - 1))

Illustration:

Input: N = 5
Output: 80
Explanation:
T_N = (a * (r ^ (N - 1))
     = (5 * (2 ^ (5 - 1))
     = (5 * 16)
     = 80

Below is the implementation of the above approach-

80

Time complexity: O(log_rn) because it is using inbuilt pow function 

Auxiliary Space: O(1) // since no extra array is used so the space taken by the algorithm is constant