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:
- 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 2: 1 + 8 + 27 + 64 + 125 = ___
Example 4: 1 + 8 + 27 + 64 + 125 + 216 + 343 = ___