Question

In a G.P the ratio of the sum of first eight to the sum of first four terms is 97:81 show that the common ratio is 2/3

Answer 1

Step-by-step explanation:

Formula,

S

n

=

r−1

ar

n

−1

Given,

S

6

S

3

=

r−1

ar

6

−1

r−1

ar

3

−1

=

152

125

(r

3

−1)(r

3

+1)

r

3

−1

=

152

125

r

3

+1

1

=

152

125

152=125r

3

+125

r

3

=

125

27

=(

5

3

)

3

∴ Common ratio r=

5

3