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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Arithemetic Sequences

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Exercise 16 Page 204

Using equivalent fractions, rewrite the terms so that all the fractions have denominator 6.

1/6, 0, -1/6

Practice makes perfect

By observing the change that occurs between consecutive terms, we can describe the pattern of the arithmetic sequence. Before we do that, let's expand the fractions to have a common denominator of 6.

Sequence	5/6, 2/3, 1/2, 1/3
Expand	5/6, 2* 2/3* 2, 1* 3/2* 3, 1* 2/3* 2
Simplify	5/6, 4/6, 3/6, 2/6

Here, we see that to get from a term to the next term we subtract 16. Therefore, the common difference of the sequence is - 16. 5/6+( - 16) ⟶4/6+( - 16) ⟶3/6+( - 16) ⟶2/6 To find the next three in the sequence, we will extend this pattern three times. 5/6& +( - 16) ⟶4/6+( - 16) ⟶3/6+( - 16) ⟶2/6 ... & +( - 16) ⟶ 1/6 +( - 16) ⟶ 0 +( - 16) ⟶ - 1/6 Therefore, the next three terms are 16, 0, and - 16.

Subchapter links

Communicate Your Answer p.199

Monitoring Progress p.200-203

Exercises p.204-206