Question

What is the sum of a 7-term geometric series if the first term is 6, the last term is 24,576, and the common ratio is −4?

−32,766

−19,662

19,662

32,766

Answer 1

847

Answer 2

First number = 6
Second number = 6*(-4) = -24
Third number = -24*(-4) = 96
etc

Answer 3

Sum of a geometric series is given by:
\[\huge S_n= \frac{a(r^n -1)}{r-1}\]
\[\huge S_7= \frac{6[(-4)^7 -1]}{r-1}\]
\[\huge S_7= \frac{6[-16384 -1]}{-4-1}\]
\[\huge S_7= \frac{6[-16385]}{-5}\]
Now solve it....