Write a formula for the general term (the nth term) of the geometric sequence.
-$$- \frac { 1 } { 3 } , \frac { 1 } { 24 } , - \frac { 1 } { 192 } , \frac { 1 } { 1536 } , \ldots$$
A) $a _ { n } = - \frac { 1 } { 3 } \left( - \frac { 1 } { 8 } \right) ^ { n }$
B) $a _ { n } = - \frac { 1 } { 3 } - \frac { 1 } { 8 } ( n - 1 )$
C) $a _ { n } = - \frac { 1 } { 8 } \left( - \frac { 1 } { 3 } \right) ^{n - 1}$
D) $a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n - 1 } + \frac { 3 } { 8 }$

Question

Quizplus · Accepted Answer

The sequence is geometric with the first term $a_1 = -\frac{1}{3}$ and a common ratio $r = \frac{\frac{1}{24}}{-\frac{1}{3}} = -\frac{1}{8}$. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, which matches choice A.

Write a Formula for the General Term (The Nth Term) −13,124,−1192,11536,…- \frac { 1 } { 3 } , \frac { 1 } { 24 } , - \frac { 1 } { 192 } , \frac { 1 } { 1536 } , \ldots−31​,241​,−1921​,15361​,…

Write a Formula for the General Term (The Nth Term) $- \frac { 1 } { 3 } , \frac { 1 } { 24 } , - \frac { 1 } { 192 } , \frac { 1 } { 1536 } , \ldots$