Question

On the first week of working out, Steve does 15 pull ups. He hopes to double that amount every month. Recursive or explicit, justify.

Answer 1

The sequence of pull-ups Steve does is an explicit sequence, as we can find each term directly. The formula to find the number of pull-ups in each month is
`a_n = a_1 * r^(n-1)`, where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the number of months.

Step-by-step explanation:

Steve's goal is to double the number of pull-ups he does every month. This is an example of an explicit sequence because we can find the value of each term directly without needing to know the previous terms. To find the number of pull-ups Steve does in each month, we can use the formula:

`an = a1 * r^(n-1)`

where an is the nth term, a1 is the first term (15 pull-ups in this case), r is the common ratio (2 in this case), and n is the number of months.

For example, to find the number of pull-ups Steve does in the second month, we can substitute n = 2 into the formula:

`a2 = 15 * 2^(2-1) = 15 * 2 = 30`

So in the second month, Steve would do 30 pull-ups.