Question 1140751
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(1) The sum of 3 consecutive numbers is 3 times the number in the middle; the sum of 5 consecutive numbers is 5 times the number in the middle.  So any number that can be written as the sum of both 3 consecutive numbers and 5 consecutive numbers must be a multiple of both 3 and 5, and therefore must be a multiple of 15.<br>
(2) The sum of 2 consecutive numbers is always odd.<br>
(3) From (1) and (2), the numbers that can be written as the sum of 2, 3, or 5 consecutive numbers are all the odd multiples of 15.<br>
(4) The largest odd multiple of 15 less than 1000 is 975.<br>
ANSWER: 975