Question

8. Sum of 1 to n natural numbers is 36, then find the value of n.​

Answer 1

The natural numbers from 1 to n are 1,2, 3, ……, n. The above sequence is an A.P. ∴ a = 1, d = 2 – 1 = 1 Sn = 36 …[Given] Now, Sn = [2a + (n – 1)d] ∴ 36 = n/2 [2(1) + (n – 1)(1)] ∴ 36 = (n/2) (2 + n – 1) ∴ 36 × 2 = n (n + 1) ∴ 72 = n (n + 1) ∴ 72 = n2 + n ∴ n2 + n – 72 = 0 ∴ n2 + 9n – 8n – 72 = 0 ∴ n(n + 9) – 8 (n + 9) = 0 ∴ (n + 9) (n – 8) = 0 ∴ n + 9 = 0 or n – 8 = 0 ∴ n = -9 or n = 8 But, n cannot be negative. ∴ n = 8 ∴ The value of n is 8.

Answer 2

answer

If  1+2+…+n=k,  then

1. √8k+1 −1= n

 8k+1−1 divided by 2 = n

√8×36+1-1 divided by 2

√289-1 divided by 2

so we get 8 as answer