### Sum of n numbers: Σ n

Find the following sums:

1 + 2 =
1 + 2 + 3 =
1 + 2 + 3 + 4 =
1 + 2 + 3 + 4 + 5 =
1 + 2 + 3 + 4 + 5 + 6 =
1 + 2 + 3 + 4 + 5 + 6 + 7 =
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 =
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 =

- _____ What is the sum of the first ten numbers?
- _____ What is the sum of the first eleven numbers?
- _____ What is the sum of the first twelve numbers?
- _____ What is the sum of the first thirteen numbers?
- _____ Is there a shortcut to finding these sums?

* ~~~ Class discussion ~~~~*
- _____ What is the sum of the first fourteen numbers?
- _____ What is the sum of the first fifteen numbers?
- _____ What is the sum of the first sixteen numbers?
- _____ What is the sum of the first seventeen numbers?
- _____ Is there a general formula to finding these sums?

* ~~~ Class discussion ~~~~*
Make a graph of the formula.

Homework:

1 + 3 =
1 + 3 + 5 =
1 + 3 + 5 + 7 =
1 + 3 + 5 + 7 + 9 =
1 + 3 + 3 + 7 + 9 + 11 =
1 + 3 + 3 + 7 + 9 + 11 +13 =

Is there a formula for the sum of odd numbers?

What is the formula for the sum of odd numbers?

2 + 4 =
2 + 4 + 6 =
2 + 4 + 6 + 8 =
2 + 4 + 6 + 8 + 10 =
2 + 4 + 6 + 8 + 10 + 12 =
2 + 4 + 6 + 8 + 10 + 12 +14 =

What is the formula for the sum of even numbers?