Write a formula for the general term (the nth term) of the geometric sequence.
-$$3 , - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$$
A) $a _ { n } = 3 \left( - \frac { 1 } { 3 } \right) ^ { n }$
B) $a _ { n } = 3 \left( - \frac { 1 } { 3 } \right) ^ { n + 1 }$
C) $a _ { n } = 3 \left( - \frac { 1 } { 9 } \right) ^ { n - 1 }$
D) $a _ { n } = 3 \left( - \frac { 1 } { 3 } \right) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

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

Write a Formula for the General Term (The Nth Term) 3,−1,13,−19,127,…3 , - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots3,−1,31​,−91​,271​,…

Write a Formula for the General Term (The Nth Term) $3 , - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$