An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 108. Find the 45^th term of this A.P.

Let A.P. has first term = a and common difference = d.

According to question,

⇒ a₅₇ = 108

⇒ a + (57 - 1)d = 108

⇒ a + 56d = 108 ………(i)

Also,

⇒ a₇ = 13

⇒ a + (7 - 1)d = 13

⇒ a + 6d = 13 ……..(ii)

Subtracting (ii) from (i) we get,

⇒ (a + 56d) - (a + 6d) = 108 - 13

⇒ a - a + 56d - 6d = 95

⇒ 50d = 95

⇒ d = 1.9

Substituting value of d in (ii) we get,

⇒ a + 6(1.9) = 13

⇒ a + 11.4 = 13

⇒ a = 13 - 11.4 = 1.6

45^th term of A.P. = a₄₅

= a + (45 - 1)d

= 1.6 + 44(1.9)

= 1.6 + 83.6

= 85.2

Hence, 45^th term of A.P. = 85.2