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

We know that

a_n = a + (n - 1)d

According to question,

⇒ a₁₇ = 2(a₈) + 5
⇒ a + 16d = 2(a + 7d) + 5
⇒ a + 16d = 2a + 14d + 5
⇒ 2a - a + 14d - 16d + 5 = 0
⇒ a - 2d + 5 = 0
⇒ a = 2d - 5.     (Eq 1)

Given, a₁₁ = 43

⇒ a + 10d = 43
⇒ 2d - 5 + 10d = 43
⇒ 12d = 43 + 5
⇒ 12d = 48
⇒ d = 4.

Putting value of d in Eq 1,

⇒ a = 2d - 5
⇒ a = 2 × 4 - 5 = 8 - 5 = 3.

∴ a_n = 3 + (n - 1) × 4 = 3 + 4n - 4 = 4n - 1.

Hence, the nth term of the A.P. is 4n - 1.