Taniya Melton
2022-10-18
Answered

Find the nth term rule for $12,4,\frac{4}{3},\frac{4}{9},...$

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Kyle Delacruz

Answered 2022-10-19
Author has **21** answers

This is a GP which first term , a, of 12 and the common ratio ,r,of 3.

The common ratio is found from dividing any two consecutive terms..

$r=\frac{{T}_{2}}{{T}_{1}}=\frac{4}{12}=\frac{1}{3}$

The general term for any GP is $T}_{n}=-a{r}^{n-1$

Substituting the values for a and r we get..

$T}_{n}=12\times {\left(\frac{1}{3}\right)}^{n-1$

The common ratio is found from dividing any two consecutive terms..

$r=\frac{{T}_{2}}{{T}_{1}}=\frac{4}{12}=\frac{1}{3}$

The general term for any GP is $T}_{n}=-a{r}^{n-1$

Substituting the values for a and r we get..

$T}_{n}=12\times {\left(\frac{1}{3}\right)}^{n-1$

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