input output
1 5
2 8
4 14
8 ?
i/o
1 5 +4
2 8 +6
4 14 +10
8 ? +16
8+16=?
(Input is doubling.)
x=input
y=output
find the slope:
m=(y2-y1)/(x2-x1)
m=(8-5)/(2-1)=3
slope intercept form:
y=mx+b
y-y1=3(x-x1)
y-5=3(x-1)
y=3x+2
Output=3(input)+2
To find the pattern and determine the output for "8" based on the previous inputs and outputs, let's examine the information given:
Input: 1 Output: 5
Input: 2 Output: 8
Input: 4 Output: 14
Looking at the outputs, we can see that each output is obtained by multiplying the input by a certain factor and then adding a constant. Let's try to figure out this pattern.
To go from an input of 1 to an output of 5, we can observe that multiplying 1 by a factor of 4 and then adding a constant of 1 gives us 5. So the pattern so far is:
Output = (Input * 4) + 1
Let's check if this pattern holds for the other examples to confirm:
Input: 2
Output = (2 * 4) + 1 = 8 (matches the given output of 8)
Input: 4
Output = (4 * 4) + 1 = 17 (not matching the given output of 14)
Since the pattern didn't hold for the input of 4, we need to reassess our approach.
Examining the differences between the outputs:
Output difference between 5 and 8: 8 - 5 = 3
Output difference between 8 and 14: 14 - 8 = 6
The output differences seem to be increasing by 3 each time. So, we can adjust our pattern to:
Output = (Input * 4) + (OutputDifference * 3)
Now, let's use this adjusted pattern to find the missing output for the input of 8:
Input: 8
Output = (8 * 4) + (6 * 3) = 32 + 18 = 50
Therefore, the missing output for the input of 8 is 50.