Find the common ratio of the geometric sequence with a first term of 18 and a $7 ^ { \text {th } }$ term of $\frac { 2 } { 81 }$ .
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 81 }$
C) $\frac { 1 } { 9 }$
D) $\frac { 1 } { 27 }$

Question

Quizplus · Accepted Answer

The formula for the $n^{th}$ term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$, where $a_n$ is the $n^{th}$ term, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. Plugging in the given values, we get $\frac{2}{81} = 18 \cdot r^{(7-1)}$, which simplifies to $\frac{2}{81} = 18 \cdot r^6$. Solving for $r$, we find $r = \frac{1}{3}$.

Find the Common Ratio of the Geometric Sequence with a First