What is the rule for this function?
Input 1, 6, 4, 7, 12
Output 4, 7, 9, 12, 17
are you certain of that 6 in the input? It looks to me that is should be 2, then the rule is add 5 to input.
The 1 and the 6 threw me off. Those are the values given. Maybe I am supposed to say there is no solution.
To find the rule for this function, we can examine the relationship between the input and output values.
Let's look at the difference between consecutive input values:
6 - 1 = 5
4 - 6 = -2
7 - 4 = 3
12 - 7 = 5
Similarly, let's look at the difference between consecutive output values:
7 - 4 = 3
9 - 7 = 2
12 - 9 = 3
17 - 12 = 5
By comparing the differences in the input and output values, we can observe a pattern. The differences in the input values are the same as the corresponding differences in the output values:
Input Differences: 5, -2, 3, 5
Output Differences: 3, 2, 3, 5
So, the rule for this function appears to be that the output values are obtained by adding the corresponding input differences to the previous output value. This means that to find the output value for a given input, we can start with the first output value (4) and add the corresponding input differences successively.
To find the missing output values, we can follow this pattern:
First input: 1
First output: 4
Second input: 6
Difference: 5
Adding the difference to the previous output (4 + 5), we get the second output: 9
Third input: 4
Difference: -2
Adding the difference to the previous output (9 - 2), we get the third output: 7
Fourth input: 7
Difference: 3
Adding the difference to the previous output (7 + 3), we get the fourth output: 10
Fifth input: 12
Difference: 5
Adding the difference to the previous output (10 + 5), we get the fifth output: 15
Therefore, the complete output sequence corresponding to the given input sequence is: 4, 9, 7, 10, 15.