Write the first five terms of the geometric sequence $a}_{1}=5,{a}_{k+1}=-2{a}_{k$ and determine the common ratio and write the nth term of the sequence as a function of n

Jaelyn Payne
2022-10-11
Answered

Write the first five terms of the geometric sequence $a}_{1}=5,{a}_{k+1}=-2{a}_{k$ and determine the common ratio and write the nth term of the sequence as a function of n

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Bobby Mcconnell

Answered 2022-10-12
Author has **8** answers

${a}_{1}=5$ and $a}_{k+1}=-2{a}_{k$

so, $a}_{2}=-2{a}_{1$

=> ${a}_{2}=-10$

Also, $a}_{3}=-2{a}_{2$

i.e. ${a}_{3}=20$

so, our terms are 5,−10,20,−40,...

Hence, 1st term 5 and common ratio -2

Now, nth term is $a{r}^{n-1}$

i.e. $5{(-2)}^{n-1})$

or, $(-\frac{5}{2})(-{2}^{n})$

With n = 7 we have:

$(-\frac{5}{2})(-{2}^{7})=320$

so, $a}_{2}=-2{a}_{1$

=> ${a}_{2}=-10$

Also, $a}_{3}=-2{a}_{2$

i.e. ${a}_{3}=20$

so, our terms are 5,−10,20,−40,...

Hence, 1st term 5 and common ratio -2

Now, nth term is $a{r}^{n-1}$

i.e. $5{(-2)}^{n-1})$

or, $(-\frac{5}{2})(-{2}^{n})$

With n = 7 we have:

$(-\frac{5}{2})(-{2}^{7})=320$

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