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

An AP consists of 50terms of which 3rd term is 12 and the last term is

1.	An AP consists of 50terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Answer» Let a , d are first term and commondifference of an A.Pnth term = Last term = a + ( n - 1 )dan = a + ( n - 1 )dNow ,It is given that ,Third term = 12a + 2d = 12 ------( 1 )Last term = 106a + 49d = 106 ---( 2 )Subtract ( 1 ) from ( 2 ) , we get47d = 94d = 2Substitute d value in equation ( 1 ) ,We geta + 2 × 2 = 12a = 12 - 4a = 829th term = a + 28da29 = 8 + 28 × 2= 8 + 56= 64 n=50 a+2d=12 - - - - 1 a49d106 - - - - - 2 by 2-1 we get, a+47d-a-2d= 106-12 47d=94 D=94/47 d=2 then a=8 a+(n-1)d=nth term 8+28×2=64