**High School Number Sense Lesson 77: Adding a Sequence of Consecutive Cubes (Starting with 1)**

I wish I would see this question a little more often, because I really like the concept. It appeared just

**3 times**on high school tests last year, with a median placement at

**question # 78**.

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To solve these problems, it will help if you already know how to add a sequence of consecutive integers (starting with 1). We haven't covered that specific variation of

**AddSequence**, but it comes in handy today. I'll cover it in a later post and leave you in suspense in the meantime...

Here is an example of today's concept:

**1 + 8 + 27 + 64**

**How to Solve:**

- Identify the last number being cubed.
- Multiply it by its neighbor.
- Divide by 2.
- Square the result.

In the example above, we are looking at the sequence of cubes of the integers from 1 to 4. So:

**4**is the last number being cubed.- 4 x 5 =
**20**. - 20 ÷ 2 =
**10**. - 10 x 10 =
**100**.

I purposefully chose to begin with this example because we can quickly add up the numbers

**1 + 8 + 27 + 64**the long way and come up with

**100**.

**Example 1:**

**1**

^{3}+ 2^{3}+ 3^{3}+ 4^{3}= ___1.

**4**is the last number being cubed.

2. 4 x 5 =

**20**

3. 20 ÷ 2 =

**10**

4. 10

^{2}=

**100**

**Example 2: 1 + 8 + 27 + 64 + 125 = ___**

**5**is the last number being cubed.

2. 5 x 6 =

**30**

3. 30 ÷ 2 =

**15**

4. 15

^{2}=

**225**

**Example 3:**

**1**

^{3}+ 2^{3}+ 3^{3}+ 4^{3}+ 5^{3}+ 6^{3}= ___1.

**6**is the last number being cubed.

2. 6 x 7 =

**42**

3. 42 ÷ 2 =

**21**

4. 21

^{2}=

**441**

**Example 4: 1 + 8 + 27 + 64 + 125 + 216 + 343 = ___**

**7**is the last number being cubed.

2. 7 x 8 =

**56**

3. 56 ÷ 2 =

**28**

4. 28

^{2}=

**784**

**Example 5:**

**1**

^{3}+ 2^{3}+ 3^{3}+ 4^{3}+ 5^{3}+ 6^{3}+ 7^{3}+ 8^{3}+ 9^{3}+ 10^{3}= ___1.

**10**is the last number being cubed.

2. 10 x 11 =

**110**

3. 110 ÷ 2 =

**55**

4. 55

^{2}=

**3025**

**Check back soon for a free worksheet to help you practice AddSeqCube.**

**Up Next for High School: FunctionRange**