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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 48 Page 319

The given rule means that, after the first term of the sequence, every term f(n) is the product of the previous term f(n-1) and 6.

f(2) = - 6 f(5) = - 1296 f(10) = - 10 077 696

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)&=- 1 f(n)&=6f(n-1), for n>1 To do so, we will use a table.

n	f(n)=6f(n-1)	f(n)
1	f( 1)=- 1	- 1
2	f( 2)=6f( 2-1) ⇕ f(2)=6 f(1)	f(2)=6( - 1) ⇕ f(2)= - 6
3	f( 3)=6f( 3-1) ⇕ f(3)=6 f(2)	f(3)=6( - 6) ⇕ f(3)= - 36
4	f( 4)=6f( 4-1) ⇕ f(4)=6 f(3)	f(4)=6( - 36) ⇕ f(4)= - 216
5	f( 5)=6f( 5-1) ⇕ f(5)=6 f(4)	f(5)=6( - 216) ⇕ f(5)= - 1296
6	f( 6)=6f( 6-1) ⇕ f(6)=6 f(5)	f(6)=6( - 1296) ⇕ f(6) - 7776
7	f( 7)=6f( 7-1) ⇕ f(7)=6 f(6)	f(7)=6( - 7776) ⇕ f(7)= - 46 656
8	f( 8)=6f( 8-1) ⇕ f(8)=6 f(7)	f(8)=6( - 46 656) ⇕ f(8)= - 279 936
9	f( 9)=6f( 9-1) ⇕ f(9)=6 f(8)	f(9)=6( - 279 936) ⇕ f(9)= - 1 679 616
10	f( 10)=6f( 10-1) ⇕ f(10)=6 f(9)	f(10)=6( - 1 679 616) ⇕ f(10)= - 10 077 696

Therefore, f(2) = - 6, f(5) = - 1296 and f(10) = - 10 077 696.

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320