Question

What would be the total number of days she used the gym membership in week 10?

Answer 1

We can see that each time the number in the sequence increases by 5, so this is a arithmetic progression.

The formula for the n-th term of an arithmetic progression is:

$a_n=a_1+(n-1)\cdot r$

The first term is 4, and the rate is 5, so we have that:

$a_n=4+(n-1)\cdot5$

If we want to find the 10th term, we just need to use n = 10:

$\begin{gathered} a_{10}=4+(10-1)\cdot5 \\ a_{10}=4+9\cdot5 \\ a_{10}=4+45 \\ a_{10}=49 \end{gathered}$

So Breanna would use her gym membership 49 days in week 10.