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Leto [7]
3 years ago
9

What is the recursive rule for the sequence 2, -1, 1/2 , -1/4

Mathematics
1 answer:
Helga [31]3 years ago
8 0

Answer:

a_n=\frac{-1}{2}a_{n-1}

a_1=2

Step-by-step explanation:

The recursive rule is a term defined in terms of other terms in the sequence.

The is a geometric sequence because it has a common ratio.

The common ratio can be found by dividing a term by previous term.

For example, all of these are equal:

\frac{-1}{2}

\frac{\frac{1}{2}}{-1}

\frac{\frac{-1}{4}}{\frac{1}{2}}

They are all equal to \frac{-1}{2}.

So we are saying:

\frac{\text{term}}{\text{previous term}}}=\frac{-1}{2}

More formally:

\frac{a_n}{a_{n-1}}=\frac{-1}{2}.

Multiply both sides by a_{n-1}:

a_n=\frac{-1}{2}a_{n-1}

When doing recursive form, you need to state a term of the sequence (or more depending on the recursive form you have).

So the first term is 2.

So the full thing for the answer is:

a_n=\frac{-1}{2}a_{n-1}

a_1=2

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