Use the Formula for the General Term of a Geometric SequenceUse the formula for the general term (the nth term)of a geometric sequence to find the indicated term of the
sequence with the given first term, $$\mathbf { a } _ { 1 }$$ , and common ratio, r.
-$$- \frac { 1 } { 6 } , \frac { 1 } { 54 } , - \frac { 1 } { 486 } , \frac { 1 } { 4374 } , \ldots$$
A) $a _ { n } = - \frac { 1 } { 6 } \left( - \frac { 1 } { 9 } \right) ^ { n }$
B) $a _ { n } = - \frac { 1 } { 6 } - \frac { 1 } { 9 } ( n - 1 )$
C) $a _ { n } = - \frac { 1 } { 9 } \left( - \frac { 1 } { 6 } \right) ^{n - 1}$
D) $a _ { n } = \left( - \frac { 1 } { 6 } \right) ^ { n - 1 } + \frac { 5 } { 27 }$

Question

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Here, $a_1 = -\frac{1}{6}$ and the common ratio $r$ can be found by dividing the second term by the first term, which gives $r = \frac{1/54}{-1/6} = -\frac{1}{9}$. Thus, the correct formula is $a_n = -\frac{1}{6} \cdot (-\frac{1}{9})^{n-1}$.

Use the Formula for the General Term of a Geometric a1\mathbf { a } _ { 1 }a1​

Use the Formula for the General Term of a Geometric $\mathbf { a } _ { 1 }$