Question

if the sum of an infinite gp and the sum of squares of its terms is 3 then common ratio of 1st series is

Answer 1

Answer :

4r = 2 or r = ½

Solution :

Let the 1st series be a + ar + ar² + .........

then the 2nd series a² +a²r² + a²r^4 + .......

their sum is given as 3

so we have,

=> a/1 - r = 3 or a = 3(1 - r)

and

=> a²/1 -r² = or a² = 3(1 - r²)

eliminating a, we get

=> {3(1 - r)}² = 3(1 - r)

=> 3(1 - r) =(1 + r) since {r ≠ 1}

=> 4r = 2 or r = ½