The 8th term of a series in A.P. is 23 and the 102nd term is 305.

Question

find series?

Answer 1

8^th term in a arithemetic series is 23 and 102^nd term is 305.

Arithemetic series form a , a + d , a + 2d , .......,a + (n - 1)d .

In arithmetic series n ^th term is [a + (n - 1)d]

Where a = first term and d  is common difference.

• 8^th term = a + 7d 

102^nd term = a + 101d

Therfore a + 7d = 23 ---------->(1)

a + 101d = 305 ----------------> (2)

• Solve the equations (1) and (2).

To elimnate the a variable subtract equation (1) from (2).

(a + 101d ) - (a + 7d ) = 305 - 23

a + 101d - a - 7d = 282

94d = 282

d = 282/94

d = 3

Substitute the d value in equation (1).

a + 7(3) = 23

a + 21 = 23

a = 23 - 21

a = 2

a + d = 5

a + 2d = 8

a + 3d = 11

a + 4d = 14

a + 5d = 17

Therfore the arithmetic series is 5, 8 , 11, 14, 17....