Find the Nth term of the series 3,10,21,36,55...

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

3, 10, 21, 36, 55...till N terms

Examples:

Input: N = 4
Output: 36

Input: N = 6
Output: 78

Approach:

From the given series, find the formula for Nth term-

1st term = 1 * ( 2(1) + 1 ) = 3

2nd term = 2 * ( 2(2) + 1 ) = 10

3rd term = 3 * ( 2(3) + 1 ) = 21

4th term = 4 * ( 2(4) + 1 ) = 36

.

.

Nth term = N * ( 2(N) + 1 ) 

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

T_N =  N * ( 2(N) + 1 ) 

Illustration:

Input: N = 10
Output: 210
Explanation: 
T_N = N * ( 2(N) + 1 )  
     = 10 * ( 2(10) + 1 ) 
     = 210

Below is the implementation of the above approach-

210

Time Complexity: O(1) // since no loop is used the algorithm takes up constant time to perform the operations

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