[Algebra]
Problem: In the series of odd numbers $1+3+5-7-9-11+13+15+17-19-21-23 \ldots$ the signs alternate every three terms, as shown. What is the sum of the first 300 terms of the series?

Solution: Since the signs alternate every three terms, it makes sense to look at the terms in groups of 6 .

The sum of the first 6 terms is $1+3+5-7-9-11=-18$.

The sum of the next 6 terms is $13+15+17-19-21-23=-18$.

In fact, the sum of each group of 6 terms will be the same, since in each group, 12 has been added to the numerical value of each term when compared to the previous group of 6 , so overall 12 has been added three times and subtracted three times.

Since we are looking for the sum of the first 300 terms, then we are looking at 50 groups of 6 terms, so the sum must be $50(-18)=-900$.

Final answer: -900