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This is essentially the sum of the first nth terms problem which is usually covered in Secondary school.

a. As the numbers are small, we can do it by trial & error.  Assuming Timothy starts with $0, then his savings is the sum of:

Week Savings that week
1 $1.20
2 $2.40
3 $3.60
4 $4.80
5 $6.00

Which totals:  $18 at the end of 5 weeks.

b. Money left after buying skateboard = $18-$17.25 = $0.75

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