Question

If the 3rd and 6th terms of an h.p are 5/16 and 1/5 then ,
the 10th term is​

Answer 1

The tenth term is

`(1)/(20)`

Explanation:

The 3rd term of an AP is 1/16.

This implies that:

`a + 2d = (5)/(16) - - - (1)`

The 6th term of an AP is 1/5.

This means that:

`a + 5d = (1)/(5) - - - (2)`

Subtract equation 1 from equation 2.

`5d - 2d = (1)/(5) - (5)/(16)`

`3d = - (9)/(80) \\ \implies \: d = - (3)/(80)`

From equation (1)

`a + 2( - (3)/(80) )= (5)/(16) \\ a - (3)/(40) = (5)/(16) \\ a = (5)/(16) + (3)/(40) \\ a = (31)/(80)`

The tenth term is:

`a + 9d = (31)/(80) + 9( - (3)/(80) ) \\ = (31)/(80) - (27)/(80) = (4)/(80) = (1)/(20)`