Question

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

Answer 1

Answer:

The tenth term is

$\frac{1}{20}$

Step-by-step explanation:

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

This implies that:

$a + 2d = \frac{5}{16} - - - (1)$

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

This means that:

$a + 5d = \frac{1}{5} - - - (2)$

Subtract equation 1 from equation 2.

$5d - 2d = \frac{1}{5} - \frac{5}{16}$

$3d = - \frac{9}{80} \\ \implies \: d = - \frac{3}{80}$

From equation (1)

$a + 2( - \frac{3}{80} )= \frac{5}{16} \\ a - \frac{3}{40} = \frac{5}{16} \\ a = \frac{5}{16} + \frac{3}{40} \\ a = \frac{31}{80}$

The tenth term is:

$a + 9d = \frac{31}{80} + 9( - \frac{3}{80} ) \\ = \frac{31}{80} - \frac{27}{80} = \frac{4}{80} = \frac{1}{20}$