An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Solution:

 Provided that,

 a3 = 12 is the 3rd term

 a50 = 106 is the 50th term

We all know that,

{{a}_{n}}=a+(n-1)d

{{a}_{3}}=a+(3-1)d

12 = a+2d ……………………………. (i)

Similarly,

{{a}_{50}}=a+(50-1)d

106 = a+49d …………………………. (ii)

  (ii) – (i), we get

94 = 47d

d = 2 = common difference

From the equation (i), we get,

12 = a+2(2)

a = 12−4 = 8

a29 = a+(29−1) d

a29 = 8+(28)2

a29 = 8+56 = 64

As a result, 64 is 29th term.