Question

Determine the nth term of the AP whose 7th term is –1 and 16th term is 17.

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

a₇ = –1

⇒ a + (7 – 1)d = –1   ...[a_n = a + (n – 1)d]

⇒ a + 6d = –1   ...(1)

Also,

a₁₆ = 17

⇒ a + 15d = 17   ...(2)

From (1) and (2), we get

–1 – 6d + 15d = 17

⇒ 9d = 17 + 1 = 18

⇒ d = 2

Putting d = 2 in (1), we get

a + 6 × 2 = –1

⇒ a = –1 – 12 = –13

∴ a_n = a + (n – 1)d

= –13 + (n – 1) × 2

= 2n – 15

Hence, the nth term of the AP is (2n – 15).