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) $a _ { n } = 3 \left( \frac { 1 } { 9 } \right) ^ { n - 1 }$
B) $a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n }$
C) $\mathrm { a } _ { \mathrm { n } } = 3 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { n } - 1 }$
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 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 choice C.

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) $3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$