Write an expression for the nth term of the sequence $\frac { 1 } { 3 } , \frac { 2 } { 9 } , \frac { 4 } { 27 } , \frac { 8 } { 81 } , \mathrm {~K}$ .
A) $a _ { n } = \frac { 2 ^ { n - 1 } } { 3 ^ { n } }$
B) $a _ { n } = \frac { 2 ^ { n + 1 } } { 3 ^ { n } }$
C) $a _ { n } = \frac { 2 ^ { n } } { 3 }$
D) $a _ { n } = \frac { 6 ^ { n + 1 } } { 4 ^ { n - 1 } }$
E) $a _ { n } = \frac { 6 ^ { n - 1 } } { 4 ^ { n } }$

Question

Quizplus · Accepted Answer

The numerator of each term is doubling (2 raised to the power of $n-1$), and the denominator is tripling (3 raised to the power of $n$), making the nth term $\frac{2^{n-1}}{3^n}$.

Write an Expression for the Nth Term of the Sequence 13,29,427,881, K\frac { 1 } { 3 } , \frac { 2 } { 9 } , \frac { 4 } { 27 } , \frac { 8 } { 81 } , \mathrm {~K}31​,92​,274​,818​, K

Write an Expression for the Nth Term of the Sequence $\frac { 1 } { 3 } , \frac { 2 } { 9 } , \frac { 4 } { 27 } , \frac { 8 } { 81 } , \mathrm {~K}$