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# What is the meaning of this?

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?

2 years, 6 months ago

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Which 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. Staff · 2 years, 6 months ago