# Sample quiz on arithmetic and geometric sequences Main home here.

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 $2$