Guess the sum if you can

Computer Science Level 1

If

1 + 2 + 3 + . . . + 250 = a 1+2+3+...+250=a

2 + 4 + 6 + . . . + 500 = b 2+4+6+...+500=b

3 + 6 + 9 + . . . + 750 = c 3+6+9+...+750=c

4 + 8 + 12 + . . . + 1000 = d 4+8+12+...+1000=d

5 + 10 + 15 + . . . + 1250 = e 5+10+15+...+1250=e

Find a + b + c + d + e a+b+c+d+e .


The answer is 470625.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

William Allen
Apr 10, 2019

b = 2 ( 1 + 2 + 3 + ⋯ + 250 ) = 2 a c = 3 a , d = 4 a , e = 5 a a + b + c + d + e = 15 a 15 a = 250 × 251 × 15 2 = 470625 b = 2(1 + 2 + 3 + \cdots + 250) = 2a \\ c = 3a , d = 4a , e = 5a \\ a + b + c + d + e = 15a \\\\ 15a = \frac{250 \times 251 \times 15}{2} = \boxed{470625}

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