Answer
The first five terms are $\frac{1}{4} \frac{1}{16} \frac{1}{64} \frac{1}{256} \frac{1}{1024}$ The sequence is geometric and the common ratio is $\frac{1}{4}$. The formula for the nth term of the sequence is $a_{n} = \frac{1}{4}(\frac{1}{4})^{n-1}$
Work Step by Step
$a_{n} = \frac{1}{4^{n}}$ is the formula we are given for the nth term of this geometric sequence. To find the first 5 terms, plug in n =1 ,2, 3... and solve. Since the resulting terms ($\frac{1}{4} \frac{1}{16} \frac{1}{64} \frac{1}{256} \frac{1}{1024}$) are each multiplied by a common number (the common ratio) which equals $\frac{1}{4}$ in this case the sequence is geometric. To express the nth term of the sequence in standard form $a_{n} = a(r)^{n-1}$ replace a with the first term and r with the common ratio: $a_{n} = \frac{1}{4}(\frac{1}{4})^{n-1}$
