Question

if the sum of infinite terms in a G.P. is 2 and the sum of their squares is 4/3 the series is
(a)1, 1/2, 1/4 ...
(b) 1,-1/2, 1/4 ....... (C) -1, -1/2, -1/4 .... (d) None​

Answer 1

Answer:

(a) will be the answer

Step-by-step explanation:

sum of infinite GP=a/1-r

that is; a/1-r=2

solving above equation we get.

a=2-2r ................eq. 1

consider a infinite GP;

a+ar+ar²+ar³...........

sum of their square is

a/1-r

here a =will be a²

r =r²

so sum will be

a²/1-r²=4/3

we get; 3a²=4-4r²...........eq.2

solving equations 1 and 2

we get r=1/2 and a=1

so series will be

1,1/2,1/4,1/8.......