Question

***WILL MEDAL***
Which sequences are geometric? Check all that apply.

–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4, –4, –12, –20, ...

Answer 1

@bibby

Answer 2

A sequence is arithmetic if:
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\[a_{n+1} - a_{n} = const \]

A sequence is geometric if:
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\[\frac{ a_{n+1} }{ a_{n} } = const\]

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EX: -2.7 , -9 , -30 , - 100, ....

Let's check if it's a geometric if not , then it's an arthmetic:

\[a_{n+1} = - 9 , a_{n} = -2.7\]

\[\frac{ a_{n+1} }{ a_{n} } = \frac{ -9}{ -2.7 } = \frac{ 10 }{ 3 }\]

\[a_{n+1} = - 30, a_{n} = -9\]


\[\frac{ a_{n+1} }{ a_{n} } = \frac{ -30}{ -9 } = \frac{ 10 }{ 3 }\]

This sequence is geometric.