# <span lang="EN-US

List of n natural number is

1, 2, 3, ……n

First term a = 1

Second term t1 = 2

Third term t3 = 3

Thus, common difference d = t3 – t2 = 3 – 2 = 1

Given Sn = 36

Thus, By using sum of nth term of an A.P. we will find it’s sum Where, n = no. of terms

a = first term

d = common difference

Sn = sum of n terms

We need to find no. of terms n   n(1 + n) = 36 × 2 = 72

n2 + n – 72 = 0

n2 + 9n – 8n – 72 = 0

n(n + 9) – 8(n + 9) = 0

(n – 8)(n + 9) = 0

n – 8 = 0 or n + 9 = 0

n = 8 or n = – 9

Since, number of terms n can’t be negative

n = 8

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