link223mh
2022-10-14
Answered

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

Answered 2022-10-15
Author has **13** answers

The geometric $n}^{\text{th}$ term is $a}_{n}=a{r}^{n-1$

Where a is the first term

$ar=4$

$a{r}^{4}=\frac{256}{27}$

$\Rightarrow a=\frac{4}{r}$

$\Rightarrow \frac{4}{r}\cdot {r}^{4}=\frac{256}{27}$

$\Rightarrow 4{r}^{3}=\frac{256}{27}$

$\Rightarrow r=\frac{4}{3}$

$\Rightarrow a=\frac{4}{r}=\frac{4}{\frac{4}{3}}=3$

$\Rightarrow {a}_{n}=3\cdot {\left(\frac{4}{3}\right)}^{n-1}$

Where a is the first term

$ar=4$

$a{r}^{4}=\frac{256}{27}$

$\Rightarrow a=\frac{4}{r}$

$\Rightarrow \frac{4}{r}\cdot {r}^{4}=\frac{256}{27}$

$\Rightarrow 4{r}^{3}=\frac{256}{27}$

$\Rightarrow r=\frac{4}{3}$

$\Rightarrow a=\frac{4}{r}=\frac{4}{\frac{4}{3}}=3$

$\Rightarrow {a}_{n}=3\cdot {\left(\frac{4}{3}\right)}^{n-1}$

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