The sum of eight consecutive (one after the other) numbers is 88. What are the numbers?

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The sum of eight consecutive (one after the other) numbers is 88. What are the numbers?

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Answer 1 · 2016-04-17T22:50:34

If we call the first number, an unknown, $n$ $n$ , then the next consecutive numbers are $n + 1, n + 2 . . . n + 7$ $n+1,n+2. . . n+7$ .

Thus, when we add all the terms, from $n$ $n$ to $n + 7$ $n+7$ together, and set that equal to $88$ $88$ , we get:

$8 n + 28 = 88$ $8n+28=88$

Note that $1 + 2 + 3 + 4 + 5 + 6 + 7 = 28$ $1+2+3+4+5+6+7=28$ .

This gives us

$8 n = 60$ $8n=60$

$n = \frac{15}{2}$ $n=15/2$

Note that this is not an integer, which leads us into shaky territory: its hard to define $\frac{15}{2}, \frac{17}{2}, \frac{19}{2} . . .$ $15/2,17/2,19/2. . .$ as "consecutive numbers," per se.

A more apt description of this would be that the sum of these $8$ $8$ numbers, all of which are $1$ $1$ away from the next highest number, have a sum of $88$ $88$ .

$\frac{15}{2} + \frac{17}{2} + \frac{19}{2} + \frac{21}{2} + \frac{23}{2} + \frac{25}{2} + \frac{27}{2} + \frac{29}{2} = 88$ $15/2+17/2+19/2+21/2+23/2+25/2+27/2+29/2=88$

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The sum of eight consecutive (one after the other) numbers is 88. What are the numbers?

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