Question

The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her firstweek of exercising.find the iterative rule

Answer 1

We are given the following sequence:

`6,18,54,162`

We notice that each term is obtained by multiplying the previous by 3, as follows:

`\begin{gathered} 6*3=18 \\ 18*3=54 \\ 54*3=162 \end{gathered}`

This is known as a geometric sequence. The iterative rule for a geometric sequence has the following form:

`a_n=a_1r^(n-1)`

Where:

`\begin{gathered} a_1=\text{ first term} \\ r=\text{ common ratio} \\ n=\text{ the place of the term we want to }\det er\min e \end{gathered}`

The common ratio is the number we have the multiply the previous term to get the next term, in this case, we have r = 3. Substituting we get:

`a_n=6(3)^(n-1)`

Since we can't simplify any further this is the iterative rule.