Write an expression for the most apparent nth term of the sequence. (Assume that $n$ begins with 1.) $\frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , - \frac { 1 } { 81 } , \frac { 1 } { 243 } , \mathrm {~K}$
A) $a _ { n } = \frac { ( - 1 ) ^ { n } } { 3 ^ { n } }$
B) $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { 3 ^ { n } }$
C) $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { 2 ^ { n } }$
D) $a _ { n } = \frac { ( - 1 ) ^ { n } } { 2 ^ { n } }$
E) $a _ { n } = \frac { 1 } { 2 ^ { n } }$

Question

Quizplus · Accepted Answer

The sequence alternates in sign, which is represented by $(-1)^{n+1}$, and the denominator increases as powers of 3, which is represented by $3^n$. Thus, the correct expression is $a_n = \frac{(-1)^{n+1}}{3^n}$.

Write an Expression for the Most Apparent Nth Term of the Sequence