Question

if the nth term of an ap is 2n+1, then what is the sum of it's first n terms

Answer 1

The sum of n terms in an AP is given by

s= n/2(2a+(n-1)d)

where :-s = sum of progression

n = number of terms

a = value of first term

d = difference between 2 terms

The nth term of an AP is [ 2n+1.] So the series is 3, 5, 7, 9,…

now, the first term in your question is 3 (2 x 1 + 1)

so, a = 3

second term is 5

third is 7, like that

so d = 2

Therefore, the sum of first n terms of the AP will be

n/2 [2 x 3 + (n-1) 2]

simplifying, we get the sum as

n [3+n-1]

The sum of the first n terms is thus = n (n+2)