**Middle School Number Sense Lesson 45: Adding a Sequence of Consecutive Even Numbers (Starting with 2)**

This concept is one of the many "special case" variations to

**AddSequence**, which is my go-to solution to almost every sequence problem. These problems showed up

**6 times**last year, with a median placement at

**question # 45**.

**Number Dojo Level: 149**

For this process to work, you need to make sure that we are dealing with

**only**even numbers, and beginning with

**2**. Here are the steps:

- Divide the last number by 2.
- Multiply the result from Step 1 by its (upper) neighbor--itself + 1.

**Example 1: 2 + 4 + 6 + 8 + 10**

- Divide the last number by 2. 10 ÷ 2 =
**5**. - Multiply 5 by (5 + 1) to get
**30**. This is your answer.

**Example 2: 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16**

- Divide the last number by 2. 16 ÷ 2 =
**8**. - Multiply 8 by 9 to get
**72**; this is your answer.

**Example 3: 2 + 4 + 6 + ... + 26**

- Divide the last number by 2. 26 ÷ 2 =
**13**. - 13 x 14 =
**182**.

**Example 4: Find the sum of the nine smallest positive even integers.**

- In this case, simply use the # given--9. (You could determine that the last # is 18, and then divide by 2 to get 9, but you're only wasting precious time).
- 9 x 10 =
**90**.

**Example 5: The sum of the smallest 12 positive even integers is ___**

- Use
**12**. - 12 x 13 =
**156**.

**Here's a free worksheet to help you practice AddSeqEven:**

addseqeven.pdf |

**Up Next for Middle School: Function**