how do i find the pattern for:
-4,8,-12,16
if the last number is negative, multiply by -1 then add 4
if the last number is positive, add 4, then multiply by -1
or how about
termn+1 = (abs(termn))*(-1)^n, where term1 = -4, n>0
oops that last line should have said:
termn+1 = (abs(termn)+4)*(-1)^n, where term1 = -4, n>0
To find the pattern for the sequence -4, 8, -12, 16, let's analyze the sequence step by step.
First, let's look at the signs of each number. We can observe that the signs alternate between negative and positive.
Now, let's break down the pattern into two cases:
Case 1: When the last number is negative
- Since the last number is negative (-4 in this case), the pattern states to multiply the absolute value of the last number by -1 and then add 4.
- In this case, the next number would be: abs(-4) * -1 + 4 = 4 * -1 + 4 = -4 + 4 = 0
Case 2: When the last number is positive
- Since the last number is positive (8 in this case), the pattern states to add 4 to the last number and then multiply it by -1.
- In this case, the next number would be: (8 + 4) * -1 = 12 * -1 = -12
Following these rules, we can generate the rest of the sequence as follows:
0, -12, 16, -20, 24, -28, ...
Alternatively, if we represent the terms as termn, we can generalize the pattern as follows:
termn+1 = (abs(termn) + 4) * (-1)^n, where term1 = -4 and n > 0
Using this general formula, you can easily find any term in the sequence by substituting the appropriate value for n.