Big Ideas Math Algebra 2, 2014
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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

Therefore, the first 6 terms of the sequence are 1, 2, 4, 7, 11 and 16.