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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 49 Page 319

The given rule means that, after the first term of the sequence, every term f(n) is the negative previous term f(n-1).

f(2) = - 8 f(5) = 8 f(10) = - 8

Practice makes perfect

We are asked to write the 2^\text{nd}, 5^\text{th} and 10^\text{th} term of a sequence, given a recursive rule.

f(1)&=8 f(n)&=- f(n-1), for n>1 To do so, we will use a table.

n	f(n)=- f(n-1)	f(n)
1	f( 1)=8	8
2	f( 2)=- f( 2-1) ⇕ f(2)=- f(1)	f(2)=- 8 ⇕ f(2)= - 8
3	f( 3)=- f( 3-1) ⇕ f(3)=- f(2)	f(3)=- ( - 8) ⇕ f(3)= 8
4	f( 4)=- f( 4-1) ⇕ f(4)=- f(3)	f(4)=- 8 ⇕ f(4)= - 8
5	f( 5)=- f( 5-1) ⇕ f(5)=- f(4)	f(5)=- ( - 8) ⇕ f(5)= 8
6	f( 6)=- f( 6-1) ⇕ f(6)=- f(5)	f(6)=- 8 ⇕ f(6)= - 8
7	f( 7)=- f( 7-1) ⇕ f(7)=- f(6)	f(7)=- ( - 8) ⇕ f(7)= 8
8	f( 8)=- f( 8-1) ⇕ f(8)=- f(7)	f(8)=- 8 ⇕ f(8)= - 8
9	f( 9)=- f( 9-1) ⇕ f(9)=- f(8)	f(9)=- ( - 8) ⇕ f(9)= 8
10	f( 10)=- f( 10-1) ⇕ f(10)=- f(9)	f(10)=- 8 ⇕ f(10)= - 8

Therefore, f(2) = - 8, f(5) = 8 and f(10) = - 8.

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320