Question

The 17^th term of AP is 5 more than twice its 8^th term. If the 11^th 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 = 2a_s +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).