Answer
The general term $a_n$ of the given sequence is given by the formula:
$a_n =15 + 5(n-1)$
After 7 weeks, her riding time would be $45$ minutes.
She will have a 1-hour riding time after 10 weeks.
Refer to the step-by-step part for the computations/solutions.
Work Step by Step
The given arithmetic sequence has $a_1 = 15$ minutes and a common difference $d=5$.
RECALL:
The $n^{th}$ term ($a_n$) of an arithmetic sequence is given by the formula
$a_n=a_1 +d(n-1)$
where $a_1$ is the first term and $d$ is the common difference.
Thus, the general term $a_n$ of the given sequence is given by the formula:
$a_n = a_1 +d(n-1)
\\a_n=15 + 5(n-1)$
Thus, after 7 weeks, her riding time would be:
$a_{7} = a_1 + d(7-1)
\\a_{7}=15+ 5(7-1)
\\a_{7}=15+5(6)
\\a_{7}=15+30
\\a_{7}=45$
Note that $1$ hour = $60$ minutes.
Thus, to find the number of weeks it will take for her to reach a 1-hour riding time, set $a_n=60$ and solve for $n$:
$a_n=15+5(n-1)
\\60=15+5(n-1)
\\60-15=5(n-1)
\\45=5(n-1)
\\\frac{45}{5} = \frac{5(n-1)}{5}
\\9=n-1
\\9+1=n
\\10=n$
Therefore, it she will have a 1-hour riding time after 10 weeks.
