**sequence**is an ordered collection of numbers or terms, such as 1, 2, 3, 4, 5. In 2016, adding numbers in a sequence showed up on the middle school number sense tests 17 times (out of 15 tests). This doesn't include special sequences such as odd or even numbers--the real total was 43 times this concept appeared in a contest. That's why I wanted to teach it early!

**Number Dojo Level: 61**

**Adding a sequence:**

- First, determine how many numbers are in the sequence.
- If there are an odd number of terms, multiply that number by the middle term.
- If there are an even number of terms, multiply that number by the
*average of the middle two terms*.

**Example 1: 4 + 7 + 10 + 13 + 16**

- There are
**5**terms, which is odd (not strange--an odd number). **10**is the middle term. 5 x 10 =**50**.- This works because the average of the first and last terms (4 & 16) is equal to the middle term (10). The average of the second and second-to-last terms (7 & 13) is also equal to the middle term, etc.

**Example 2: 14 + 13 + 12 + 11 + 10 + 9 + 8**

- There are
**7**terms, which is an odd number. - The middle term is
**11**. 7 x 11 =**77**.

**Example 3: 4 + 6 + 8 + 10 + 12 + 14**

- There are
**6**terms--an even number. - Look at the middle 2 terms (8 & 10) and take the average (
**9**). - Multiply the # of terms (6) by 9 to get
**54**.

**Example 4: 38 + 28 + 18 + 8**

- There are
**4**terms--an even number. - The average of the middle 2 terms (28 & 18) is
**23**. 4 x 23 =**92**. - Notice that the average of the first & last terms (38 & 8) is also 23. This is helpful when some of the terms are left out of the question and replaced by an ellipsis (...).

**Example 5: 3 + 6 + 9 + ... + 24 + 27**

- This sequence consists of multiples of 3. Based on the last number being 27, you can determine that there are
**9**terms. - Since you can't easily tell what the middle term is, just take the average of the first and last terms (3 & 27), which is
**15**. 9 x 15 =**135**.

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

addsequence.pdf |

**Up Next: DivWhole**