Mathematics: Which sequence displays exponential behavior? 1). 5, 25, 125, 625 ... 2). 15, 18, 21, 24.. 3). 3, 6, 9, 12 ... 4). 4, 16, 32, 64...

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Which sequence displays exponential behavior? 1).

noahah3

21.01.2022

1) is the only geometric sequence.

Geometric sequence is a sequence that has exponential behavior.

Step-by-step explanation:

You are looking for a common ratio.

That is you are trying to see which one produces the same number no matter what term you choose divided by it's previous term.

$\frac{\text{ term}}{\text{previous term}}=\text{ same number }$

1) So we want to see if the following holds true. If it does, then it is geometric (has exponential behavior).

$\frac{25}{5}=\frac{125}{25}=\frac{625}{125}$

Simplify:

5=5=5

So one looks good.

2) $\frac{18}{15}=\frac{21}{18}=\frac{24}{21}$

Reduce:

$\frac{6}{5}=\frac{7}{6}=\frac{8}{7}$

These are obviously not the same number. Therefore, this is not geometric.

3) $\frac{6}{3}=\frac{9}{6}=\frac{12}{9}$

The only integer is 6/3 which is 2 and the other two aren't so we don't have the same number across the board. Therefore, this one is not geometric.

4) $\frac{16}{4}=\frac{32}{16}=\frac{64}{32}$

Simplify:

4=2=2

Not the same across the board so this is not geometric either.

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