Give a rule for finding the first of four consecutive odd integers if you know the sum of the four integers.

This ones a bit of a trick question, since whether the integers are even or odd doesn't really matter. What does matter, is that consecutive odd integers are 2 numbers apart (as are consecutive even integers).

So again, if the first of the odd integers is the variable n

the consecutive odd integers after it can be written as:

n+2 , n+4, etc...

So the sum of four consecutive odd integers can be written as:

sum = n + (n+2) + (n+4) + (n+6)

Simplify:

sum = 4n + 12

And finally rearrange to solve for n:

= n

This can also be written as:

- 3 = n

Whichever way you prefer.