Question

List 4 numbers that are following an Exponential pattern, explain how you knowthe pattern is Exponential.

Answer 1

A sequence follows an exponential pattern when each successive number increases (or decreases) by the same percent.

Then, we can define the intial value as 3 and we want the common ratio to be 2, meaning that each term doubles its previous value:

`\begin{gathered} a_1=3 \\ a_2=2\cdot a_1=2\cdot3=6 \\ a_3=2\cdot a_2=2\cdot6=12 \\ a_4=2\cdot a_4=2\cdot12=24 \end{gathered}`

We know it follows an exponential pattern because the ratio between consecutive terms has a constant value:

`(a_n)/(a_(n-1))=2`

for any value of n.

Answer:

3, 6, 12, 24 are four terms of an exponential pattern where each term is the double of the previous one.

As the ratio between consecutive terms is constant, we know we have a exponential sequence or pattern.