Question

The sum of infinite terms gp is 4 an the sum of their cubes is 192 find thw g

Answer 1

sum of infinite terms of GP is a/(1-r)
where a = 1st term and r is common ratio
4 = a/(1-r) Equation 1
now sum of cubes of gp is 192
192 = a^3/(1-r^3) Equation 2

Now Cubing both sides of equation 1
64 = a^3/(1-r)^3 Equation 3

Divide Equation 2 by Equation 3
3 = (1-r)^3/(1-r^3)
3 = (1+r+r^2)
r^2+r-2 =0
r = 1 or -2(selected)

a = 12

GP is
12, -24, 48, -96.....