Question

the sum of the first three terms of a geometric series is 64 and the sum of the next three terms is 27. Find the exact value of sum to infinity of the series.

Answer 1

a1 - first element
a1 * q - second
a1 * q^2 - third
etc

so sum of first three:

a1 + a1 * q + a1 * q^2 = 64
a1(1+q+q^2) = 64

sum of next three:
a1 * q^3 + a1*q^4 + a1*q^5 = 27
a1*q^3(1+q+q^2)=27

can you do it now ?