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

Given, a₁₇ = 5 + 2(a₈) (i)

a₁₁ = 43

a + 10d = 43 (ii)

a₈ = a + 7d

a₁₇ = a + 16d

= 43 – 10d + 16d [from (ii)]

= 43 + 6d

Putting the value of a₈ and a₁₇ in (i), we get

43 + 6d = 5 + 2(a + 7d)

43 – 5 = 2a + 14d – 6d

38 = 2a + 8d

38 = 2(43 – 10d) + 8d [from (ii)]

38 = 86 – 20d + 8d

38 = 86 – 12d

12d = 86 – 38

d = 4

From (ii), a = 43 – 10d

= 43 – 10 * 4 = 43 – 40 = 3

We know, n^th term of A.P., a_n = a + (n -1) d

= 3 + (n – 1) 4

= 3 + 4n – 4 = 4n – 1

Hence, n^th term is 4n – 1