Question

12) Find the sum, S7 for the geometric series {1 + 5 + 25 + - + 15625).

Answer 1

Understanding:

The sum of a geometric series is, $a+ar+ar^2+ar^3+...$, with a being the start point and r is the common ratio. We can also use the following formula to make life easier $S_n=a\frac{1-r^n}{1-r}$, a is your start point, r is the common ratio, and n is the number of terms, which in our case is S7.

Solution:

Our start point is 1, $a=1$,

The common ratio is 5, $r=5$,

And finally, the number of terms is 7, $n=7$.

$S_n=a\frac{1-r^n}{1-r} \\=(1)\frac{1-(5)^{(7)}}{1-(5)} \\=\frac{1-78125}{1-5} \\=\frac{-78124}{-4}\\=19531$

The answer is [A] 19531.

Answer 2

Answer:

a

Step-by-step explanation: