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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

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Exercise 12 Page 825

Start by finding the formula, then use it to find the next two terms.

Next Two Terms: - 216 and - 343
Formula: a_n=- n^3
Explicit or Recursive? Explicit

Practice makes perfect

We want to find a formula for the given sequence. - 1, - 8 - 27, - 64, - 125, ...

Notice that all of the terms in the sequence are cube numbers. We will use this to find the formula.

a_1	a_2	a_3	a_4	a_5	...	a_n
- 1	- 8	- 27	- 64	- 125	...	—
- 1^3	- 2^3	- 3^3	- 4^3	- 5^3	...	- n^3

Since the formula describes the n^(th) term using the number n, it is an explicit formula. Let's use it to find the next two terms.

a_n=- n^3
a_6=- 6^3	a_7=- 7^3
a_6=- 216	a_7=- 343

The next two terms in the sequence are - 216 and - 343.

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Exercises p.825