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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 4 Page 442

The given rule means that, after the first term of the sequence, every term a_n is the difference between the doubled previous term a_(n-1) and 1.

a_1=4, a_2=7, a_3=13, a_4=25, a_5=49, a_6=97

Practice makes perfect

We are asked to write the first 6 terms of a sequence, given a recursive rule.

a_1&=4 a_n&=2a_(n-1)-1 To do so, we will use a table.

n	a_n=2a_(n-1)-1	2a_(n-1)-1	a_n
1	a_1=4	-	4
2	a_2=2a_(2-1)-1	2 a_1-1=2( 4)-1	7
3	a_3=2a_(3-1)-1	2 a_2-1=2( 7)-1	13
4	a_4=2a_(4-1)-1	2 a_3-1=2( 13)-1	25
5	a_5=2a_(5-1)-1	2 a_4-1=2( 25)-1	49
6	a_6=2a_(6-1)-1	2 a_5-1=2( 49)-1	97

Therefore, the first 6 terms of the sequence are 4, 7, 13, 25, 49 and 97.

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450