Question

The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.

Answer 1

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

a₁₇ = 2a₈ + 5   ...(Given)

∴ a + 16d = 2(a + 7d) + 5   ...[a_n = a + (n – 1)d]

⇒ a + 16d = 2a + 14d + 5 

⇒ a – 2d = –5   ...(1)

Also, 

a₁₁ = 43   ...(Given)

⇒ a + 10d = 43   ...(2)

From (1) and (2), we get

–5 + 2d + 10d = 43

⇒ 12d = 43 + 5 = 48

⇒ d = 4 

Putting d = 4 in (1), we get

a – 2 × 4 = –5

⇒ a = –5 + 8 = 3

∴ a_n = a + (n – 1)d

= 3 + (n – 1) × 4

= 4n – 1

Hence, the nth term of the AP is (4n – 1).