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

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Alaina Contreras · Accepted Answer

Step 1
If we call the first number, an unknown, n, then the next consecutive numbers are
$n + 1, n + 2 \dots n + 7$
Thus, when we add all the terms, from n to $n + 7$ together, and set that equal to 88, we get:
$8 n + 28 = 88$
Note that
$1 + 2 + 3 + 4 + 5 + 6 + 7 = 28$
This gives us
$8 n = 60$
$n = \frac{15}{2}$
Note that this is not an integer, which leads us into shaky territory: its hard to define $\frac{15}{2}, \frac{17}{2}, \frac{19}{2} \dots$ as "consecutive numbers," per se.
A more apt description of this would be that the sum of these 8 numbers, all of which are 1 away from the next highest number, have a sum of 88.
$\frac{15}{2} + \frac{17}{2} + \frac{19}{2} + \frac{21}{2} + \frac{23}{2} + \frac{25}{2} + \frac{27}{2} + \frac{29}{2} = 88$

The sum of eight consecutive (one after the other) numbers

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