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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 10 Page 447

The given rule means that, after the second term of the sequence, every term f(n) is the product of the previous two terms f(n-1) and f(n-2).

f(1)=2, f(2)=3, f(3)=6, f(4)=18, f(5)=108, f(6)=1944

Practice makes perfect

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

f(1)&=2, f(2)=3 f(n)&=f(n-1) * f(n-2) To do so, we will use a table.

n	f(n)=f(n-1)* f(n-2)	f(n-1) * f(n-2)	f(n)
1	f( 1)=2	-	2
2	f( 2)=3	-	3
3	f( 3)=f( 3-1)* f( 3-2)	f(2)* f(1)= 3* 2	6
4	f( 4)=f( 4-1)* f( 4-2)	f(3) * f(2)= 6* 3	18
5	f( 5)=f( 5-1) * f( 5-2)	f(4)* f(3) = 18* 6	108
6	f( 6)=f( 6-1) * f( 6-2)	f(5)* f(4) = 108* 18	1944

Therefore, the first 6 terms of the sequence are 2, 3, 6, 18, 108 and 1944.

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450