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# arithmetic series

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

Jul 28, 2022

#1
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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