document.write( "Question 251848: Find the sum of all the integers divisible by 7 between 32 and 5000.
\n" ); document.write( "a) 1,514,285 b) 1,515,285 c) 1,615,185 d) 1,786,715 e) none of these \n" ); document.write( "

Algebra.Com's Answer #183595 by jsmallt9(3758) $\"\"$ $\"About$

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Since the closest multiple of 7 to 5000 is 4998 (714*7), what we are looking for is:
\n" ); document.write( "35 + 42 + 49 + ... + 4992 + 4998
\n" ); document.write( "If we factor out 7 I think we'll see something we can figure out:
\n" ); document.write( "7(5 + 6 + 7 + ... + 713 + 714)
\n" ); document.write( "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.
\n" ); document.write( "The sum all the natural numbers up to n is given by the formula: $\"S%5Bn%5D+=+%28n%28n%2B1%29%29%2F2\"$ . So we can find the sum of 1 + 2 + 3 + ... + 714 with: $\"714%2A715%2F2%29+=+255255\"$ . 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:
\n" ); document.write( "7*255245 = 1786715 which is answer (d) \n" ); document.write( "

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