To find the nth term of a geometric sequence, you can use the formula:
\[ a_n = a_1 \cdot r^{(n-1)} \]
where:
- \(a_n\) is the nth term,
- \(a_1\) is the first term,
- \(r\) is the common ratio,
- \(n\) is the term number.
In this case, you are given that the fifth term (\(a_5\)) is \(1/16\) and the common ratio \(r\) is \(1/4\).
Using the formula for the fifth term:
\[ a_5 = a_1 \cdot r^{(5-1)} = a_1 \cdot r^4 \]
Substituting \(r = \frac{1}{4}\):
\[ a_5 = a_1 \cdot \left(\frac{1}{4}\right)^4 \] \[ = a_1 \cdot \frac{1}{256} \]
We know that \(a_5 = \frac{1}{16}\). Therefore, we can set up the following equation:
\[ a_1 \cdot \frac{1}{256} = \frac{1}{16} \]
To solve for \(a_1\), multiply both sides by \(256\):
\[ a_1 = \frac{1}{16} \cdot 256 \] \[ = 16 \]
Now, we have \(a_1 = 16\) and \(r = \frac{1}{4}\).
Now we can express the nth term of the geometric sequence:
\[ a_n = 16 \cdot \left(\frac{1}{4}\right)^{(n-1)} \]
Thus, the formula to find the nth term of this geometric sequence is:
\[ a_n = 16 \cdot \left(\frac{1}{4}\right)^{(n-1)} \]