Sequences and Series

Need help on part C please! See attached image for question. The mark scheme says the answer is 500 but I have no clue how they are getting to that

Look based on the top recurrence relation you can swap out the n for k to get

$a_{k+1} = 5 - k a_k$

which is equivalent to saying

$a_{k+1} + k a_k = 5$

So really when you are being asked to calculate

it's the same as being asked to sum 5 exactly 100 times.

This is a one mark question so you are not expected to write much here this is all there is to it.