5. Recursion and Iteration
Sign In
Use the initial value as the input of a function rule. This will give us the first output value.
56, 680, 8168
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)=12x+8 | x_(n+1) |
|---|---|---|---|
| 0 | x_0= 4 | 12 x_0+8=12( 4)+8 | 56 |
| 1 | x_1= 56 | 12 x_1+8=12( 56)+8 | 680 |
| 2 | x_2= 680 | 12 x_2+8=12( 680)+8 | 8168 |
| 3 | x_3= 8168 | - | - |
Therefore, the first three iterates of the function are 56, 680 and 8168.