Question

In a geometric progression if the ratio of the sum of first 5

Answer 1

As we learnt in

Common ratio of a GP (r) -

The ratio of two consecutive terms of a GP

- wherein

eg: in 2, 4, 8, 16, - - - - - - -

r = 2

and in 100, 10, 1, 1/10 - - - - - - -

r = 1/10

Let the G.P is G, Gr, Gr2.................

Given that \frac{G+Gr+Gr^{2}+Gr^{3}+Gr^{4}}{\frac{1}{G}+\frac{1}{Gr}+\frac{1}{Gr^{2}}+\frac{1}{Gr^{3}}+\frac{1}{Gr^{4}}}= 49

\therefore G^{2}\frac{\left ( 1+r+r^{2}+r^{3}+r^{4} \right )}{\left ( 1+r+r^{2}+r^{3}+r^{4} \right )}= 49

\therefore G^{2}r^{4}= 49

\therefore Gr^{2}= 7

\therefore 35-G=7

G=28