It's true that you can easily add them up directly, especially with the
technology available today. But perhaps this student is not allowed to do it
that way.
It is well known that the sum
which is easy to proved by induction. For n=24
Writing out the first 3 terms of that summation
Summing the first 3 terms:
Subtract 36 from all three sides:
That's with what she got, finding the sum directly instead of with a well-known
formula.
Edwin