What's the process if the input numbers are 1,2,3,4,5 and the output numbers are 2,5,10,17,26
since the differences are 3,5,7,9
and the 2nd differences are all 2, you expect a quadratic.
A little thought shows that
y = x^2+1
if the input number is 1 2 3 4 5 what will be the output number
To understand the process behind obtaining the output numbers from the given input numbers, let's examine the pattern:
- Starting with the first input number, which is 1, the corresponding output number is 2.
- The second input number, which is 2, leads to an output number of 5.
- The third input number, which is 3, gives an output number of 10.
- The fourth input number, which is 4, results in an output number of 17.
- Lastly, the fifth input number, which is 5, generates an output number of 26.
By analyzing these pairs of input and output numbers, we can identify that the pattern is not a simple arithmetic progression (where each output number is obtained by adding a constant difference to the input number). Instead, it seems to follow a more complex pattern.
One way to determine the pattern is by considering the differences between consecutive output numbers. Let's calculate these differences:
- The difference between 2 and 5 is 3.
- The difference between 5 and 10 is 5.
- The difference between 10 and 17 is 7.
- The difference between 17 and 26 is 9.
Looking at these differences, we observe that they are consecutive odd numbers starting from 3: 3, 5, 7, 9.
This suggests that the process to obtain the output numbers might involve the following steps:
1. Start with the input number.
2. Square the input number.
3. Multiply the squared input number by the corresponding odd number from the sequence 3, 5, 7, 9, ...
Let's apply this process to each of the given input numbers to validate our hypothesis:
- For the first input number, 1:
- Square the number: 1^2 = 1.
- Multiply by 3: 1 * 3 = 3.
- The output number is 3, but according to the given pattern, it should be 2. Therefore, our hypothesis is incorrect.
Based on this analysis, it seems that the proposed process of squaring the input number and multiplying it by the consecutive odd numbers does not align with the given pattern. Consequently, we need more information to accurately determine the correct process or pattern for obtaining the output numbers.