Question

Find the twelfth term of a sequence where the first term is $256$ and the common ratio is $r=\frac{1}{4}$.

Short answer

The the twelfth term of a sequence is equal to$\frac{1}{4^7}$.

Step-by-step solution

Step 1. Given information

The first term is $256$ and the common ratio is $r=\frac{1}{4}$.

Step 2. Find the twelfth term of a sequence. 

Let $a$denotes the first term of the sequence.

$\begin{array}{rcl}a& =& 256\\ r& =& \frac{1}{4}\\ a_n& =& a{r}^{n-1}\end{array}$

$\begin{array}{rcl}{a}_{12}& =& 256{\left(\frac{1}{4}\right)}^{12-1}\\ & =& 4^4{\left(\frac{1}{4}\right)}^{11}\\ & =& \frac{1}{4^7}\end{array}$