Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • If the sum of first six terms of any G.P. is equal to 9 times the sum of the first threeterms, then find the common ratio of the G.P.​

If the sum of first six terms of any G.P. is equal to 9 times the sum of the first threeterms, then find the common ratio of the G.P.​

Answers (1)

Let $S_{n}$ be sum first n terms of G.P. and r be common ratio
Formula for sum of n terms of G.P. is given by S_{n}=\frac{a\left(r^{n}-1\right)}{r-1}$

\text{Given} : S_{6}=9 \times S_{3}$\\ $S_{6}=\frac{a\left(r^{6}-1\right)}{r-1}=9 \times \frac{a\left(r^{3}-1\right)}{r-1}$\\ $\Rightarrow r^{6}-1=9\left(r^{3}-1\right)$ \\ $\Rightarrow\left(r^{3}-1\right)\left(r^{3}+1\right)=9\left(r^{3}-1\right)$\\ $\Rightarrow r^{3}=-1+9=8$\\ $\Rightarrow r=2$ \\ 

Posted by

Satyajeet Kumar

View full answer

Similar Questions

Latest Question