Sample quiz on arithmetic and geometric sequences
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  1. The enumeration $0,2,4,8,\cdots$ represents $\cdots$?
    a geometric sequence with a common ratio of $2$
    a geometric sequence with a first term of $0$
    an arithmetic sequence with a common difference of $2$
    neither a geometric sequence nor an arithmetic sequence
  2. What is the $n$th term of the sequence $2,6,18,54,\cdots$?
    $2(3)^{n-1}$
    $2(3)^{n+1}$
    $3(2)^{n-1}$
    $2(2)^{n-1}$
  3. What is the $n$th term of the sequence $-2,-5,-8,-11,\cdots$?
    $1+3n$
    $1-3n$
    $-1+3n$
    $-1-3n$
  4. How many terms are in the sequence $2,-1,-4,-7,\cdots,-46$?
    $16$
    $17$
    $18$
    $19$
  5. The third and seventh terms of an arithmetic sequence are $7$ and $27$, respectively. What is the first term?
    $-2$
    $-3$
    $-4$
    $-5$
  6. The third and fifth terms of a geometric sequence are $18$ and $162$, respectively. Find possible value(s) of the common ratio.
    $2$
    $\pm 3$
    $-3$
    $3$
  7. The three-term sequence $1,(x+1),(x^2+2x+1)$ is geometric. Identify a possible restriction on $x$.
    $x\neq 1$
    $x\neq 2$
    $x\neq -2$
    $x\neq -1$
  8. Find the number of terms in the sequence $-2,1,-\frac{1}{2},\frac{1}{4},\cdots,-\frac{1}{32}$
    $6$
    $7$
    $8$
    $9$
  9. A sequence defined recursively by $T_1=2, T_{n}=T_{n-1}-2$ is likely to be $\cdots$?
    a geometric sequence with a first term of $-2$
    a geometric sequence with a common ratio of $-2$
    an arithmetic sequence with a common difference of $-2$
    an arithmetic sequence with a common difference of $2$
  10. The even numbers $2,4,6,8,\cdots$ form
    an arithmetic sequence with a common difference of $4$
    an arithmetic sequence with a common difference of $2$
    a geometric sequence with a first term of $2$
    a geometric sequence with a common ratio of $2$