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Big Ideas Math Algebra 2, 2014 View details

5. Using Recursive Rules with Sequences

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Exercise 3 Page 442

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

f(0)=1, f(1)=2, f(2)=4, f(3)=7, f(4)=11, f(5)=16

Practice makes perfect

We are asked to write the first 6 terms of a sequence, given a recursive rule. f(0)&=1 f(n)&=f(n-1)+n To do so, we will use a table.

n	f(n)=f(n-1)+n	f(n-1)+n	f(n)
0	f( 0)=1	-	1
1	f( 1)=f( 1-1)+ 1	f(0)+1= 1+1	2
2	f( 2)=f( 2-1)+ 2	f(1)+2= 2+2	4
3	f( 3)=f( 3-1)+ 3	f(2)+3= 4+3	7
4	f( 4)=f( 4-1)+ 4	f(3)+4= 7+4	11
5	f( 5)=f( 5-1)+ 5	f(4)+5= 11+5	16