find the middle term of the A.P. 6, 13, 20, …, 216. (CBSE 2015)

The given A.P. is 6, 13, 20, …, 216

Let n be the number of terms,

Common difference, d = 13-6 = 7

First term, a = 6

Last term, a_n = 216,

a_n = a + (n-1)d

⇒ 216 = 6 + (n-1)7

⇒ 210 = (n-1)7

⇒ 30 = n-1

⇒ n = 31(Odd)

So, we have to find a₁₆ for this A.P.

a₁₆ = 6 + (16-1)7

⇒ a₁₆ = 6 + 15 × 7

⇒ a₁₆ = 6 + 105

⇒ a₁₆ = 111

So, The middle term of this A.P. is 111.