How does this sum work out? What is the role of 5n in the problem? Doesn't the formula sum all terms from first to last via (#terms)*(first+last)/2? So then aren't we summing 41 terms from 500 to 700? But which terms are we summing?

I'm a little lost, please help.

Thanks in advance.

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TopNewestWhich step/sentence are you confused by:

1) The multiple of 5 in the interval \( [500,700] \) are \(500, 505, 510, \ldots , 700 \).

2) This is an arithmetic progression with initial term 500, and common difference 5.

3) The formula for a general term in this progression is \( a_n = 500 + (n-1) \times 5 \).

4) There are 41 terms in this sequence.

5) The sum of this arithmetic progression is \( \frac{ 41 ( 500 + 700) } {2} = 24600 \).

6) This is the sum \(S\) that is asked for in the question.

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