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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 29 Page 319

Can you find the common ratio and the first term just by looking at the explicit formula?

$a_{1} = 7, a_{n} = 3 a_{n - 1}$

Practice makes perfect

The explicit formula of a geometric sequence combines the information provided by the two equations of the recursive form into a single equation.

Recursive : Explicit : a_{1} = a_{1}; a_{n} = r \cdot a_{n - 1} a_{n} = a_{1} r^{n - 1}

In these formulas,

r

is the common ratio and

a_{1}

is the first term. Looking at the given explicit formula, we can identify the common ratio

r

and the value of the first term

a_{1} .

a_{n} = 7 (3)^{n - 1}

We can see that

3

is the common ratio and the first term is

7 .

Now we have enough information to form a recursive formula for this sequence.

a_{1} = a_{1} a_{n} = r \cdot a_{n - 1} \Rightarrow a_{1} = 7 a_{n} = 3 a_{n - 1}

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320