5. Recursion and Iteration
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Use the initial value as the input of a function rule. This will give us the first output value.
-45, 273, -1635
We are asked to write the first three iterates of a function, given a function rule and an initial value.
| n | x_n | f(x)=-6x+3 | x_(n+1) |
|---|---|---|---|
| 0 | x_0= 8 | -6 x_0+3=-6( 8)+3 | -45 |
| 1 | x_1= -45 | -6 x_1+3=-6( -45)+3 | 273 |
| 2 | x_2= 273 | -6 x_2+3=-6( 273)+3 | -1635 |
| 3 | x_3= -1635 | - | - |
Therefore, the first three iterates of the function are -45, 273 and -1635.