What is the rule for this function?
Input 1 output 3
Input 2 output 5
Input 4 output 9
Input 5 output 11
Input 10 output 21
Input 12 output 25
Please help thanks
http://www.jiskha.com/display.cgi?id=1354418711
an = 2 * n + 1
For n = 1
a1 = 2 * 1 + 1 = 2 + 1 = 3
For n = 2
a2 = 2 * 2 + 1 = 4 + 1 = 5
etc.
Looking at the given inputs and outputs, it seems that the rule for this function involves adding 2 to the input number, and then adding another 1 if the input number is odd.
So, the step-by-step rule for this function can be described as follows:
1. Take the input number.
2. Add 2 to the input number.
3. If the input number is odd, add 1.
4. The final result is the output.
For example:
- Input 1:
- Add 2 to 1: 1 + 2 = 3
- Since 1 is odd, add 1: 3 + 1 = 4
- Output: 4
- Input 2:
- Add 2 to 2: 2 + 2 = 4
- Since 2 is even, no need to add 1.
- Output: 4
- Input 12:
- Add 2 to 12: 12 + 2 = 14
- Since 12 is even, no need to add 1.
- Output: 14
To identify the rule for this function, we need to look for a pattern in the input-output pairs. Let's analyze the given inputs and outputs:
Input 1 --> Output 3
Input 2 --> Output 5
Input 4 --> Output 9
Input 5 --> Output 11
Input 10 --> Output 21
Input 12 --> Output 25
Observing the pattern, we can see that every input value is increasing by 1, while the corresponding output value is increasing by 2.
Therefore, we can conclude that the rule for this function is that the output is obtained by multiplying the input by 2 and adding 1.
To verify this rule, we can apply it to a few other values:
Input 3 --> Output 7 (3*2 + 1 = 7)
Input 6 --> Output 13 (6*2 + 1 = 13)
Input 8 --> Output 17 (8*2 + 1 = 17)
The rule seems to hold true for these additional examples, supporting our initial conclusion.