#### Explanation:

We are working with an arithmetic series, where each term representswthe total in the account after $15$ is added each week.

The sequence is $\text{ "50," "65," "80," } 95 \ldots \ldots . 500$

We are looking for $\left(n - 1\right)$ weeks

After 1 week, we have the 2nd term,
After 2 weeks we have the 3rd term ....

We know that T_n = $500," " a = 50," " d = 15 $T n = a + \left(n - 1\right) d$$50 + \left(n - 1\right) 15 = 500$$\left(n - 1\right) 15 = 500 - 50 = 450$$n - 1 = \frac{450}{15} = 30$Therefore after 30 weeks he has $500