Question

The 17^th term of an A.P. is 5 more than twice its 8^th term. If 11^th term of A.P. is 43; then find its n^th term.

Answer 1

Given,

⇒ a₁₇ = 5 + 2a₈ and a₁₁ = 43

[Here, a₈, a₁₁ and a₁₇ are 8^th, 11^th and 17^th term respectively]

Since,

n^th term of an A.P., a_n = a + (n – 1)d,

where a = first term

d = common difference

∴ a + (17 – 1)d = 5 + 2{a + (8 – 1)d}

⇒ a + 16d = 5 + 2a + 14d

⇒ 2d – a = 5   ...(i)

Also, a + (11 – 1)d = 43

⇒ a + 10d = 43   ...(ii)

Solving equations (i) and (ii), we get

a = 3 and d = 4

Hence, n^th term would be a_n = 3 + (n – 1)4 = 4n – 1.