Consecutive odd integers must be a difference of 2.
The traditional solution as taught in school is to let one value be "x" and the next value must be two more, or "x + 2" and the third value must be "x + 2 + 2" which is "x + 4".
x
x + 2
x + 2 + 2
3x + 2 + 2 + 2 = 3x + 6 which you are told equals -45 in this problem.
So:
3x + 6 = -45
Add -6 to both sides of the equation to get:
3x = -51
Then, divide by 3 to get:
x= -17
Add 2 to get:
x + 2 = -15
Add another 2 to get:
x + 2 + 2 = -13
Final answer:
-13 + -15 + -17 = -45
Now....for a shortcut solution (Some students consider this an easier solution than the traditional solution explained above.).....
If all three values were the middle value, divide the sum total (-45) by the sample size (3) to get the value of each number (-15).
And since this arithmetic sequence has a constant difference of "2", simply add and subtract 2 from -15 to get:
-15 + 2 = -13
-15 - 2 = -17
(as if "one outside number gave 2 to the other outside number")
-13 + -15 + -17
I hope this was helpful for you, Emily. Have a happy holiday season.