Question

If the sum of first six terms of g.P. Is equal to 9 times the sum of the first three terms then find the common ratio . Brainly .Com

Answer 1

common ratio=2

hope this answer will help you.

Answer 2

Given: The sum of first six terms of G.P. is equal to 9 times the sum of the first three terms

To find: Common ratio

Step-by-step explanation:

As we know $S_n= \dfrac{a(r^n-1)}{r-1}$ is the sum of n terms of G.P. where a is first term , and r is common ratio

As given

The sum of first six terms of G.P. is equal to 9 times the sum of the first three terms we have

$S_6= 9S_3\\\\\Rightarrow \dfrac{a(r^6-1)}{r-1} =9\times \dfrac{a(r^6-1)}{r-1}\\\\\Rightarrow r^6-1= 9(r^3-1)\\\\\Rightarrow \dfrac{r^6-1}{r^3-1} =9\\\\\Rightarrow \dfrac{(r^3-1)(r^3+1)}{r^3-1} =9\\\\\Rightarrow r^3+1=9 \\\\\Rightarrow r^3=8 \\\\\Rightarrow r= \sqrt[3]{8} =2$

Hence the common ratio is 2