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.
-$$\frac { 1 } { 5 } , - \frac { 1 } { 40 } , \frac { 1 } { 320 } , - \frac { 1 } { 2560 } , \ldots$$
A) $a _ { n } = \frac { 1 } { 5 } \left( - \frac { 1 } { 8 } \right) ^ { n }$
B) $a _ { n } = \frac { 1 } { 5 } - \frac { 1 } { 8 } ( n - 1 )$
C) $\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 8 } \left( - \frac { 1 } { 5 } \right) ^ { n - 1}$
D) $a _ { n } = \left( \frac { 1 } { 5 } \right) ^ { n - 1 } - \frac { 9 } { 40 }$

Question

Quizplus · Accepted Answer

The sequence is geometric with the first term $a_1 = \frac{1}{5}$ and a common ratio $r = -\frac{1}{8}$ (since each term is $-\frac{1}{8}$ times the previous term). The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, which matches choice A when substituting $a_1 = \frac{1}{5}$ and $r = -\frac{1}{8}$.

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 $\mathbf { a } _ { 1 }$