Find n-th term of series 1, 3, 6, 10, 15, 21...

Given a number n, find the n-th term in the series 1, 3, 6, 10, 15, 21...

Examples

Input 3
Output 6

Input 4
Output 10

The given series represent triangular numbers which are sums of natural numbers.

[Naive approach] Using Loop - O(n) time and O(1) space

The series sums the first n natural numbers, with each term adding one more number. The nth term is the sum of the first n natural numbers.

10

[Expected Approach] Using Formula - O(1) time and O(1) space

The pattern in this series is n^th term is equal to sum of (n-1)^th term and n.

n = 2
2^nd term equals to sum of 1^st term and 2 i.e
A2 = A1 + 2 = 1 + 2 = 3
Similarly,
A3 = A2 + 3 = 3 + 3 = 6 and so on..

We get: 

A(n) = A(n - 1) + n
= A(n - 2) + n + (n - 1)
= A(n - 3) + n + (n - 1) + (n - 2)
.
.
.
= A(1) + 2 + 3... + (n-1) + n

A(n) = 1 + 2 + 3 + 4... + (n - 1) + n = n(n + 1) / 2
i.e A(n) is sum of First n natural numbers.

10