Question

If the seventh term of an AP is 1/9 and its ninth term is 1/7, find its 63^rd term.

Answer 1

Let a be the first term and d be the common difference of the given A.P.

Given:

`a_7=1/9`

`a_9=1/7`

`a_7=a+(7-1)`

`d=1/9`

`=>a+6d=1/9 .........(1)`

`a_9=a+(9-1)d=1/7`

`=>a+8d=1/7......(2)`

Subtracting equation (1) from (2), we get:

2d=2/63

=>d=1/63

Puttingd=1/63 in equation (1), we get:

`a+(6xx1/63)=1/9`

`=>a=1/63`

`∴ a_63=a+(63-1)d=1/63+62(1/63)`

`=63/63=1`

Thus 63^rd term   of the given A.P. is 1.