# SOLUTION: Find the sum of all the integers divisible by 7 between 32 and 5000. a) 1,514,285 b) 1,515,285 c) 1,615,185 d) 1,786,715 e) none of these

Algebra ->  Algebra  -> Divisibility and Prime Numbers -> SOLUTION: Find the sum of all the integers divisible by 7 between 32 and 5000. a) 1,514,285 b) 1,515,285 c) 1,615,185 d) 1,786,715 e) none of these      Log On

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 Question 251848: Find the sum of all the integers divisible by 7 between 32 and 5000. a) 1,514,285 b) 1,515,285 c) 1,615,185 d) 1,786,715 e) none of theseFound 2 solutions by richwmiller, jsmallt9:Answer by richwmiller(9135)   (Show Source): You can put this solution on YOUR website!this was solved yesterday Answer by jsmallt9(3296)   (Show Source): You can put this solution on YOUR website!Since the closest multiple of 7 to 5000 is 4998 (714*7), what we are looking for is: 35 + 42 + 49 + ... + 4992 + 4998 If we factor out 7 I think we'll see something we can figure out: 7(5 + 6 + 7 + ... + 713 + 714) Inside the parentheses we see most of the numbers from 1 to 714. We are just missing 1, 2, 3 and 4. So if we can figure out this sum then we can multiply by 7 and have our answer. The sum all the natural numbers up to n is given by the formula: . So we can find the sum of 1 + 2 + 3 + ... + 714 with: . Now we need to "remove 1, 2, 3 and 4: 255255 - 1 - 2 - 3 - 4 = 255245. So 255245 is the sum of (5 + 6 + 7 + ... 714). Now we just multiply this by 7: 7*255245 = 1786715 which is answer (d)