Question

Find the middle term of the A.P. 7, 13, 19, ...., 247.

Answer 1

In this A.P., a = 7, d = 13 – 7 = 6

And t_n = 247

∵ t_n = a + (n – 1)d

∴ 247 = 7 + (n – 1)6

⇒ 6(n – 1) = 240

⇒ n – 1 = 40

⇒ n = 41

Hence, the middle term = `(n + 1)/2`

= `(41 + 1)/2`

= `42/2`

= 21