# If the nth term of an A.P be (2n - 1), then the sum of its first n terms will be____

An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.

## Sum of N Terms of A.P.

For any progression, the sum of n terms can be easily calculated. For an AP, the sum of the first n terms can be calculated if the first term and the total terms are known. The formula for the arithmetic progression sum is explained below:

Consider an AP consisting of “n” terms.

 S = n/2[2a + (n − 1) × d]

Formula to find the sum of AP when first and last terms are given as follows:

 S = n/2 (first term + last term)

### Solution

For AP,

an = a+ (n-1)d = 2n-1

a1 = 2-1 = 1

a2 = 4-1 = 3

Common difference , d = 3-1 = 2

Sum of n terms = (n/2)(2a + (n-1)d)

= (n/2)(2+(n-1)2)

= (n/2)(2+2n-2)

= (n/2)2n

= n2

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