Danika Mckay

2022-10-12

Write the expression for the nth term of the geometric sequence ${a}_{1}=64,r=-\frac{1}{4},n=10$

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indivisast7

Expert

the nth term for a geometric sequence is
$•x{a}_{n}=\frac{a\left(1-{r}^{n}\right)}{1-r}←a={a}_{1}$
$⇒{a}_{n}=\frac{64\left(1-{\left(-\frac{1}{4}\right)}^{n}\right)}{1+\frac{1}{4}}$
$⇒{a}_{n}=\frac{256}{5}\left(1-{\left(-\frac{1}{4}\right)}^{n}\right)$

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