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.

Let a and d be the first term and common difference of the AP Given: a₁₇ = 2 × a₈ + 5

a₁₁ = 43

To find: n^th term = a_n

Consider a11 = 43

⇒ a + (11 - 1)d = 43

⇒ a + 10d = 43 ………….. (1)

Consider a₁₇ = 2 × a₈ + 5

⇒ a + (17 - 1)d = 2[a + (8 - 1)d] + 5

⇒ a + 16d = 2a + 14d + 5

⇒ - a + 2d = 5 ……………….(2)

Adding equation (1) and equation (2), we get

12d = 48

⇒ d = 4

∴ from equation (1), we get,

a = 43 - 10d

= 43 - 40

= 3

Now, n^th term is given by:

a_n = a + (n - 1)d

⇒ a_n = 3 + (n - 1)4

⇒ a_n = 4n - 1

Therefore, n^th term is given by (4n - 1).