Question

Find the middle term(s) of an A.P. 9, 15, 21, 27, …, 183.

Answer 1

A.P = 9, 15, 21, 27, …, 183

No. of terms in an A.P. is

n = `("l" - "a")/"d" + 1`

a = 9, l = 183, d = 15 – 9 = 6

∴ n = `(183 - 9)/6 + 1`

= `174/6 + 1`

= 29 + 1 = 30

∴ No. of terms = 30.

The middle must be 15^th term and 16^th term.

∴ t₁₅ = a + (n – 1)d

= 9 + 14 × 6

= 9 + 84

= 93

t₁₆ = a + 15d

= 9 + 15 × 6

= 9 + 90 = 99

∴ The middle terms are 93, 99.