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arsen [322]
1 year ago
15

-5, 20, -80, 320, ... is a geometric sequence a. Find the common ratio, b. Write its recursive rule c. Write its explicit rule.W

hat is the common ratio and explicit rule?
Mathematics
1 answer:
mario62 [17]1 year ago
5 0

a.

In order to find the common ratio, we just need to divide a term by the term that comes before it.

So using the terms 20 and -5, we have:

\text{ratio}=\frac{20}{-5}=-4

b.

The recursive rule can be found with the formula:

a_n=a_{n-1}\cdot q

Where an is the nth term and q is the ratio. So we have:

a_n=a_{n-1}\cdot(-4)

c.

The explicit rule can be written as:

a_n=a_1\cdot q^{n-1}

Where an is the nth term, a1 is the first term and q is the ratio. So:

a_n=-5\cdot(-4)^{n-1}

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