Question

The sum of the first two terms of a GP is 5/3 and the sum of infinity of the series is 3. The common ratio
is

Answer 1

Given-

Sum of first two terms of GP= 5/3

Sum of infinity series = 3

To find-

common ratio

Solution-

let first term of GP be "a"

and

it's common ratio be "r"

ATQ

Sum of first two terms=

a+ar=5/3

taking a common we get

a(1+r)=5/3 ...(1)

Sum of infinite series=

a/(1-r) = 3 ...(2)

solving equation 1 and 2 we get

a = 5/3(1+r)

5/3(1-r^2)=3

5/9= 1-r^2

r^2= 4/9

r= +_ 2/3

a= 1,5

hence common ration = r = +_ 2/3