Question

Find the middle term of the AP 10, 7, 4, ..., (–62).

Answer 1

The given AP is 10, 7, 4, ..., –62.

First term, a = 10

Common difference, d = 7 – 10 = –3

Suppose these are n terms in the given AP. Then,

a_n = –62

⇒ 10 + (n – 1) × (–3) = –62    ...[a_n = a + (n – 1)d]

⇒ –3(n – 1) = –62 – 10 = –72

⇒ `n - 1 = 72/3 = 24`

⇒ n = 24 + 1 = 25

Thus, the given AP contains 25 terms.

∴ Middle term of the given AP

= `((25 + 1)/2)`th term 

= 13th term 

= 10 + (13 – 1) × (–3)

= 10 – 36 

= –26 

Hence, the middle term of the given AP is –26.