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Dennis_Churaev [7]
3 years ago
14

Which sequence is modeled by the graph below? Points: (2,8) (3,4) (4,2) (5,1)

Mathematics
1 answer:
asambeis [7]3 years ago
7 0

Answer:

a_n=16 \cdot (\frac{1}{2})^{n-1}

Step-by-step explanation:

This sequence is geometric because while x is going up by 1, the y sequence has a common ratio.

That is, term/previous equals same number per consecutive y terms.

So 1/2=2/4=4/8 is the common ratio.

The first term is when x=1. We can find this y by figuring out what we can multiply to our common ratio, 1/2, to get the next term,8.

Since 8(2)=16, then the first term is 16.

In general,

y=a_1 \cdot (r)^{x-1}

Or if preferred:

a_n=a_1 \cdot (r)^{n-1}

where a_1 is first term and r is common ratio.

Plug in information:

a_n=16 \cdot (\frac{1}{2})^{n-1}

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