# Write a rule for the nth term of the geometric sequence given the two terms a_2=4, a_5=256/27

Write a rule for the nth term of the geometric sequence given the two terms ${a}_{2}=4,{a}_{5}=\frac{256}{27}$
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Remington Wells
The geometric ${n}^{\text{th}}$ term is ${a}_{n}=a{r}^{n-1}$
Where a is the first term
$ar=4$
$a{r}^{4}=\frac{256}{27}$
$⇒a=\frac{4}{r}$
$⇒\frac{4}{r}\cdot {r}^{4}=\frac{256}{27}$
$⇒4{r}^{3}=\frac{256}{27}$
$⇒r=\frac{4}{3}$
$⇒a=\frac{4}{r}=\frac{4}{\frac{4}{3}}=3$
$⇒{a}_{n}=3\cdot {\left(\frac{4}{3}\right)}^{n-1}$