hall & knight GP question

let gp be --> a,ar,ar² ,..... ∞
therefore T_n = ar^n-1 = arⁿ +arⁿ⁺¹ .... ∞
for n=1, T₁= ar +ar² +...∞ = ar1-r =a (first term of series)

therefore 2r=1 or r=1/2;

now from given info- a+ar=5;
or 3a/2=5
a=10/3

hence we can find the series!

i m getting r=1/4
and a=4

ya i think kunl is rite

coz a + ar = 5

then acc. to quesn

a = ar + ar² + ar³ .................

a =3 ar / 1-r

so that gives r = 1/4 and a=4...

so the series is 4 , 1 , 1/4................