# Write the recursive formula for each geometric sequence. 640, 160, 40, 10, 2.5, ...

Write the recursive formula for each geometric sequence. 640, 160, 40, 10, 2.5, ...
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brawnyN
Use the recursive formula of a geometric sequence given by:
${a}_{n}=r\left({a}_{n}-1\right)$ where r is the common ratio.
Find the common ratio:
$r=\frac{160}{640}=\frac{40}{160}=\frac{10}{40}=\frac{2.5}{10}=\frac{1}{4}$
Substibute $r=\frac{1}{4}:$
${a}_{n}=\frac{1}{4}\left({a}_{n}-1\right)$
the recursive formula is ${a}_{n}=\frac{1}{4}\left({a}_{n}-1\right)$, where the initial condition is ${a}_{1}=640$