Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$
A) $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n } }$
B) $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n - 1 } }$
C) $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n + 1 } }$
D) $a _ { n } = \frac { 4 ^ { n } } { 5 ^ { n } }$
E) $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n } }$

Question

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)   $\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$  
A) $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n } }$
B) $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n - 1 } }$
C) $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n + 1 } }$
D) $a _ { n } = \frac { 4 ^ { n } } { 5 ^ { n } }$
E) $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n } }$

Quizplus · Accepted Answer

The numerator of each term is $4^{n-1}$ (since it starts at $4^0 = 1$ for $n=1$, and increases by a power of 4 for each subsequent term), and the denominator is $5^n$ (since it starts at $5^1 = 5$ for $n=1$, and increases by a power of 5 for each subsequent term).

Write an Expression for the Apparent Nth Term of the Sequence.(Assume