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What is 75 + 72 + 69 + 66 + ... + 21 + 18 + 15 + 12 + 9 + 6 + 3?

 Jul 28, 2022
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Rewrite as: \((3 \times 25) + (3 \times 24) + (3 \times 23) + \cdot \cdot \cdot +(3 \times 4) + (3 \times 3) + (3 \times 2) + (3 \times 1) \)

 

Factor out the 3: \(3(1 + 2+3+4+5+ \cdot \cdot \cdot 22 + 23 + 24 + 25 )\)

 

The sum of the inside part is \(25 \times 26 \div 2 = 325\)

 

So the sum of everything is \(325 \times 3= \color{brown}\boxed{975}\)

 Jul 28, 2022

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