Question

Please help! A geometric series has a sum of 9,837. The common ratio is 3 and the first term is 9. How many terms are in the series?

Answer 1

The geometric series is \[a+ar+ar^2+ar^3 +\ldots\] If you have n terms, then the sum of these n term is given by
\[a+ar+ar^2+\ldots+ar^{n-1}= a\frac{1-r^n}{1-r}=S\]
You hav ebeen told that the first term is 9 (so \(a=9\)) and that the common ration is 3 (r=3) and that the sum is 9837 (so S=9837). Fill in these values and then rearrange to get n, the number of terms in the series.

Answer 2

You should get n=7