Question

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

Answer 1

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

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

`8n+28=88`

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

This gives us

`8n=60`

`n=15/2`

Note that this is not an integer, which leads us into shaky territory: its hard to define `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` numbers, all of which are `1` away from the next highest number, have a sum of `88`.

`15/2+17/2+19/2+21/2+23/2+25/2+27/2+29/2=88`