The first and the last terms of an A.P. are 1 and 11 respectively. If the sum of its terms is 36, then the number of terms is :

1. 6

2. 7

3. 8

4. 9

Given,

a = 1

l = 11

Let no. of terms be n.

S_n = 36

We know that,

⇒ S_n = $\dfrac{n}{2}$ (a + l)

⇒ 36 = $\dfrac{n}{2}$ (1 + 11)

⇒ 36 × 2 = n(12)

⇒ n = $\dfrac{36 \times 2}{12}$

⇒ n = 6.

Hence, option 1 is the correct option.