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.
42, 212, 1062
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) = 5x+2 | x_(n+1) |
|---|---|---|---|
| 0 | x_0= 8 | 5 x_0+2=5( 8)+2 | 42 |
| 1 | x_1= 42 | 5 x_1+2=5( 42)+2 | 212 |
| 2 | x_2= 212 | 5 x_2+2=5( 212)+2 | 1062 |
| 3 | x_3= 1062 | - | - |
Therefore, the first three iterates of the functions are 42, 212 and 1062.