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

1.	An AP consists of 50 terms of which 3d term is 12 and the last term is 106. Find the 29term.
Answer» Let a , d are first term and common difference of an A.P nth term = Last term = a + ( n - 1 )d an = a + ( n - 1 )d Now , It is given that , Third term = 12 a + 2d = 12 ------( 1 ) Last term = 106 a + 49d = 106 ---( 2 ) Subtract ( 1 ) from ( 2 ) , we get 47d = 94 d = 2 Substitute d value in equation ( 1 ) , We get a + 2 × 2 = 12 a = 12 - 4 a = 8 29th term = a + 28d a29 = 8 + 28 × 2 = 8 + 56 = 64

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

Answer»

Let a , d are first term and common

difference of an A.P

nth term = Last term = a + ( n - 1 )d

an = a + ( n - 1 )d

Now ,

It is given that ,

Third term = 12

a + 2d = 12 ------( 1 )

Last term = 106

a + 49d = 106 ---( 2 )

Subtract ( 1 ) from ( 2 ) , we get

47d = 94

d = 2

Substitute d value in equation ( 1 ) ,

We get

a + 2 × 2 = 12

a = 12 - 4

a = 8

29th term = a + 28d

a29 = 8 + 28 × 2

= 8 + 56

= 64