input 1 output -2
input 2 output 8
input 3 output -32
input 4 output 128
what is the rule? please help.
To determine the rule for the given input-output pattern, let's analyze the sequence of outputs.
The input-output sequence seems to follow a pattern of alternating signs and increasing powers of 2. Let's break it down:
- For input 1, the output is -2. (-2 is equal to -2^1)
- For input 2, the output is 8. (8 is equal to -2^2)
- For input 3, the output is -32. (-32 is equal to -2^3)
- For input 4, the output is 128. (128 is equal to -2^4)
We can observe that the output is obtained by:
1) Taking the alternate signs (+ or -)
2) Raising -2 to the power of the input number (2^input)
Based on this analysis, the rule for the given input-output pattern can be defined as follows:
Rule: The output is obtained by taking the alternate signs and raising -2 to the power of the input number.
Using this rule, you can find the output for any given input by following these steps:
1) Determine the power of -2 based on the input number.
2) Apply the alternate sign based on the position of the input number (odd or even).
3) Evaluate the result by performing the necessary calculations based on the rule.
For example, to find the output for input 5, following the rule would yield:
Output for input 5: -(2^5) = -32
Remember to apply the alternate sign (-) when the input number is odd, and no sign (positive) when the input number is even.