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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 3 Page 318

The recursive equation for an arithmetic sequence is $a_{n} = a_{n - 1} + d .$ The recursive equation for a geometric sequence is $a_{n} = r \cdot a_{n - 1} .$

Geometric sequence

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We will use the following facts.

The recursive equation for an arithmetic sequence is $a_{n} = a_{n - 1} + d .$
The recursive equation for a geometric sequence is $a_{n} = r \cdot a_{n - 1} .$

We are given the recursive rule below.

a_{1} = 2, a_{n} = 7 \cdot a_{n - 1}

Since the recursive equation is of the form

a_{n} = r \cdot a_{n - 1},

it represents a geometric sequence.

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320