Sample quiz on geometric series
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  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 $S_{10}=29524$?
    $-2$
    $-3$
    $3$
    $2$