To find the explicit rule for the number of complaints received in the nth month, we can observe the pattern in the given data. The number of complaints increases by 4 each month.
So, we can write the explicit rule as follows:
Number of complaints (n) = 18 + 4(n - 1)
To find the number of months it will take for the complaints to reach 126, we can set up an equation:
18 + 4(n - 1) = 126
Simplifying the equation:
4(n - 1) = 126 - 18
4(n - 1) = 108
n - 1 = 27
n = 28
Therefore, it will take 28 months for the number of complaints to reach 126.