# Write the first five terms of the geometric sequence a_1=5,a_(k+1)=−2a_k and determine the common ratio and write the nth term of the sequence as a function of n

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
${a}_{1}=5$ 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. $5{\left(-2\right)}^{n-1}\right)$
or, $\left(-\frac{5}{2}\right)\left(-{2}^{n}\right)$
With n = 7 we have:
$\left(-\frac{5}{2}\right)\left(-{2}^{7}\right)=320$