The A.P. 6, 13, 20, …, 216 has 31 terms. The middle term of the A.P. is :

1. 91

2. 97

3. 107

4. 111

Given,

A.P. 6, 13, 20, …, 216

n = 31

Middle term of A.P. = $\dfrac{n + 1}{2}$

= $\dfrac{31 + 1}{2}$

= $\dfrac{32}{2}$

= 16th term.

We know that,

nth term of A.P. :

∴ T_n = a + (n - 1)d

Now we have,

a = 6

d = 13 - 6 = 7

n = 16

⇒ T₁₆ = 6 + (16 - 1)(7)

= 6 + (15)7

= 6 + 105

= 111.

Hence, option 4 is the correct option.