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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 2 Page 442

The given rule means that, after the first term of the sequence, every term a_n is the product of the term a_(n-1) and 0.5.

a_0=162, a_1=81, a_2=40.5, a_3=20.25, a_4=10.125, a_5=5.0625

Practice makes perfect

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

a_0&=162 a_n&=0.5a_(n-1) To do so, we will use a table.

n	a_n=0.5a_(n-1)	0.5a_(n-1)	a_n
0	a_0=162	-	162
1	a_1=0.5a_(1-1)	0.5 a_0=0.5( 162)	81
2	a_2=0.5a_(2-1)	0.5 a_1=0.5( 81)	40.5
3	a_3=0.5a_(3-1)	0.5 a_2=0.5( 40.5)	20.25
4	a_4=0.5a_(4-1)	0.5 a_3=0.5( 20.25)	10.125
5	a_5=0.5a_(5-1)	0.5 a_4=0.5( 10.125)	5.0625

Therefore, the first 6 terms of the sequence are 162, 81, 40.5, 20.25, 10.125 and 5.0625.

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450