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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 8 Page 318

The given rule means that, after the first term of the sequence, every term a_n is the difference between the previous term a_(n-1) and 5.

Sequence: 10, 5, 0, - 5, - 10, and - 15
Graph:

Practice makes perfect

We are asked to write the first 6 terms of a sequence, given a recursive rule. a_1&=10 a_n&=a_(n-1)-5, for n ≥ 2

To do so, we will use a table.

n	a_n=a_(n-1)-5	a_(n-1)-5	a_n
1	a_1=10	-	10
2	a_2=a_(2-1)-5	a_1-5= 10-5	5
3	a_3=a_(3-1)-5	a_2-5= 5-5
4	a_4=a_(4-1)-5	a_3-5= -5	- 5
5	a_5=a_(5-1)-5	a_4-5=- 5-5	- 10
6	a_6=a_(6-1)-5	a_5-5=- 10-5	- 15

Therefore, the first 6 terms of the sequence are 10, 5, 0, - 5, - 10, and - 15. Let's graph these points!

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320