Question

Sum of infinite numbers of terms in GP is 20 and sum of their square is 100. Find the common ratio of GP

Answer 1

Let terms of GP be a, ar, ar2

where a = first term, r = common ratio

S∞ = a/1-r

Therefore, a/1-r = 20

a = 20(1-r)

Also, a2 = 100(1 - r2)

Answer 2

Answer:

Common ratio of the G.P is $\frac{3}{5}$.

Step-by-step explanation:

Let a = first term of G.P and r = common ratio of G.P

Then G.P is $a,ar,ar^2$.

Given S∞ = 20 = $\frac{a}{1-r}$ = 20

Also $a^2=a^2r^2+a^2r^4+..\;to$ ∞ = 100

$\rightarrow\;\frac{a^2}{1-r}\;=\;100\;\;\;a^2\;=\;400(1=r^2)$

We get $100(1-r)(1+r)\;=\;400(1-r)^2$

$\rightarrow\;1+r\;=\;4=4r$

$\rightarrow\;\;5r\;=\;3$

$\rightarrow\;r\;=\frac{3}{5}$

∴ Common ratio of the G.P is $\frac{3}{5}$.