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 =
  1. _____ What is the sum of the first ten numbers?
  2. _____ What is the sum of the first eleven numbers?
  3. _____ What is the sum of the first twelve numbers?
  4. _____ What is the sum of the first thirteen numbers?
  5. _____ Is there a shortcut to finding these sums?
~~~ Class discussion ~~~~

  1. _____ What is the sum of the first fourteen numbers?
  2. _____ What is the sum of the first fifteen numbers?
  3. _____ What is the sum of the first sixteen numbers?
  4. _____ What is the sum of the first seventeen numbers?
  5. _____ Is there a general formula to finding these sums?
~~~ Class discussion ~~~~

Make a graph of the formula. graph

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?