Question

The first and third of term GP are 10 and20 respectively and the common ratio is positive.

Find the common ratio.

Answer 1

The first and third of term GP are 10 and20 respectively and the common ratio is positive

Answer 2

Answer:

a=1

a

3

=ar

2

=r

2

a

5

=ar

4

=r

4

Given a

3

+a

5

=90

∴r

2

+r

4

=90

⇒r

4

+r

2

=90

⇒r

4

+r

2

−90=0

⇒r

2

=

2

−1+

1+360

=

2

−1±

361

=

2

−1±19

=−10or9

∴r=±3(Taking real roots