# Sample quiz on geometric series Main home here.

1. Let $a$ and $r$ have their usual meanings. The sum of the first $n$ terms of a geometric series can be given by $\cdots$?
$S_{n}=\frac{a(r^n-1)}{1-r}$
$S_{n}=\frac{a(r^{n-1})}{r-1}$
$S_{n}=\frac{a(r^n-1)}{r-1}$
$S_{n}=\frac{a(r^n+1)}{r-1}$
2. What is the sum of the first $10$ terms of the geometric series $1+2+4+8+\cdots$?
$1023$
$1024$
$2046$
$512$
3. Find the sum of the geometric series $2+6+18+54+\cdots+4374$
$2180$
$2187$
$6561$
$6560$
4. A geometric series has $a=3$ and $r=4$. How many terms must be taken so that $S_{n}=16,777,216$?
$13$
$12$
$11$
$10$
5. Find the sum of the series $2+(-4)+8+(-16)+\cdots+2048$
$4094$
$1366$
$4096$
$1364$
6. What is the sum of the first $12$ terms of the series $2+1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots$?
$\frac{4095}{1024}$
$\frac{4095}{4096}$
$\frac{4096}{4095}$
$\frac{1024}{4095}$
7. If a geometric series is such that $r-a=1$, then the sum of the first $n$ terms is $\cdots$?
$S_{n}=1-r^n$
$S_{n}=a(r^n-1)$
$S_{n}=r^n-1$
$S_{n}=a(1-r^n)$
8. Find the sum of the first $8$ terms of the series $\frac{1}{3}+\frac{2}{9}+\frac{4}{27}+\frac{8}{81}+\cdots$
$\frac{6561}{6305}$
$\frac{2059}{2187}$
$\frac{2187}{2059}$
$\frac{6305}{6561}$
9. Find the sum of the first $9$ terms of the series $3+(-3)+3+(-3)+3+\cdots$
$3$
$6$
$0$
$-3$
10. What is the common ratio of a geometric series in which $a=2$ and $S_{10}=29524$?
$-2$
$-3$
$3$
$2$