Integers

The sum of 6 consecutive integers is 171. Find the smallest of the integers

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asked by Ana
  1. From the problem statement, we know that some 6 integers must sum to 171. To get an idea of what these numbers are, start by dividing 171 by 6. This yields 28.5, which is what the average of our numbers are.

    Here we can construct numbers close to this interval-- the problem did state these would be consecutive. Remember that we want the average to be 28.5, so start with 27, 28, 29. 30, 26, since they are the same distance from our current average 28 will preserve this average, so these are also numbers in the interval. We know that these numbers must sum to 171, so sum our current 5 numbers and subtract that from 171, yielding 31.

    The numbers in question are therefore 26, 27, 28, 29, 30, 31. The smallest is 26.

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    posted by Alex
  2. or, using what you know about arithmetic progressions,

    6/2 (2a+5*1) = 171
    a = 26

    so the numbers are as shown above.

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    posted by Steve
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    posted by ntsobi

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