Which formula can be used to find the nth term of a geometric sequence where the fifth term is (1)/(16) and the common ratio is (1)/(4) a_(n)=16((1)/(4))^n-1 a_(n)=(1)/(16)((1)/(4))^n-1 a_(n)=(1)/(4)(16)^n-1 a_(n)=(1)/(4)((1)/(16))^n-1

To find the nth term of a geometric sequence, we can use the formula:<br /><br />$a_{n} = a_{1} \cdot r^{n-1}$<br /><br />where $a_{1}$ is the first term and $r$ is the common ratio.<br /><br />In this case, we are given that the fifth term is $\frac{1}{16}$ and the common ratio is $\frac{1}{4}$. We can use this information to find the first term and then use the formula to find the nth term.<br /><br />Let's substitute the given values into the formula:<br /><br />$\frac{1}{16} = a_{1} \cdot \left(\frac{1}{4}\right)^{5-1}$<br /><br />Simplifying the right side of the equation:<br /><br />$\frac{1}{16} = a_{1} \cdot \left(\frac{1}{4}\right)^{4}$<br /><br />$\frac{1}{16} = a_{1} \cdot \frac{1}{256}$<br /><br />To solve for $a_{1}$, we can multiply both sides of the equation by 256:<br /><br />$256 \cdot \frac{1}{16} = 256 \cdot a_{1} \cdot \frac{1}{256}$<br /><br />$16 = a_{1}$<br /><br />Now that we have found the first term, we can substitute it back into the formula to find the nth term:<br /><br />$a_{n} = 16 \cdot \left(\frac{1}{4}\right)^{n-1}$<br /><br />Therefore, the correct formula to find the nth term of the geometric sequence is:<br /><br />$a_{n} = 16 \cdot \left(\frac{1}{4}\right)^{n-1}$<br /><br />So, the correct answer is:<br /><br />$a_{n} = 16 \cdot \left(\frac{1}{4}\right)^{n-1}$