5. Using Recursive Rules with Sequences
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f(0)=1, f(1)=2, f(2)=4, f(3)=7, f(4)=11, f(5)=16
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.