Exercise 9 Page 447

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

f(0)&=2, f(1)=4 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)
0	f( 0)=2	-	2
1	f( 1)=4	-	4
2	f( 2)=f( 2-1)-f( 2-2)	f(1)- f(0)= 4- 2	2
3	f( 3)=f( 3-1)-f( 3-2)	f(2) - f(1)= 2- 4	- 2
4	f( 4)=f( 4-1) - f( 4-2)	f(3)- f(2) = - 2- 2	- 4
5	f( 5)=f( 5-1) - f( 5-2)	f(4)- f(3) = - 4- ( - 2)	- 2

Therefore, the first 6 terms of the sequence are 2, 4, 2, - 2, - 4 and - 2.