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PLEASE HELP WHATS THIS (there’s also a quadratic option)

PLEASE HELP WHATS THIS (there’s also a quadratic option)-example-1

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Answer:

D. Quadratic

Explanation:

It can be helpful to look at differences between terms when trying to decide what sort of sequence you have.

Here, the first differences are ...

8-6 = 2

14 -8 = 6

24 -14 = 10

38 -24 = 14

These are not constant (not a linear sequence), and they don't have a common ratio (not an exponential sequence).

However, they do have a common difference:

6 -2 = 4

10 -6 = 4

14 -10 = 4

This set of differences can be called "second differences." The fact they are constant means the sequence can be modeled by a second-degree polynomial, a quadratic.

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Additional comment

Ordinarily, you might look at the ratio of terms to see if they have a common ratio, indicating a sequence is exponential. An exponential sequence will have the same common ratio between terms at any level of differences. So, we can look at the ratios of first- or second-differences to determine if a sequence is exponential. Sometimes those numbers are smaller, and easier to deal with.

If the exponential sequence has an added value (is translated vertically), the original terms won't have a common ratio, but the differences will.

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