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Big Ideas Math Algebra 2, 2014

BI

Big Ideas Math Algebra 2, 2014 View details

5. Using Recursive Rules with Sequences

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Exercise 11 Page 444

Is it possible to find the common difference and the first term just by looking at the recursive rule?

$a_{n} = 16 n - 28$

Practice makes perfect

The explicit rule of an arithmetic sequence combines the information provided by the two equations of the recursive rule into a single equation.

Recursive : Explicit : a_{n} = a_{n - 1} + d; a_{1} = a_{1} a_{n} = a_{1} + (n - 1) d

In these rules,

d

is the common difference and

a_{1}

is the first term. Looking at the given recursive rule, we can identify the common difference

d

and the value of the first term

a_{1} .

a_{1} = - 12, a_{n} = a_{n - 1} + 16

We can see that

16

is the common difference and the first term is

- 12 .

Now we have enough information to form an explicit rule for this sequence.

a_{n} = a_{1} + (n - 1) d

$a_{1} = - 12$ , $d = 16$

a_{n} = - 12 + (n - 1) 16

Distribute $16$

a_{n} = - 12 + 16 n - 16

Subtract term

a_{n} = 16 n - 28

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450