n is even and an <0
If n is even and an < 0, it means that n is a negative even number
If n is even and an < 0, it means that n is a negative even number.
To understand this better, let's break down the information provided:
1. n is even: This means that n can be evenly divided by 2. In other words, when n is divided by 2, there is no remainder.
2. an < 0: This inequality tells us that the product of a and n is less than 0. Any number multiplied by a negative number will result in a negative number.
Since n is even, it can be expressed as n = 2k, where k is an integer. We can substitute this expression into the inequality:
a(2k) < 0
Now, we have two scenarios to consider:
Case 1: a > 0
If a is positive, then multiplying it with 2k (which is an even number) will always give a positive result. However, we need the product to be negative, so this case is not possible.
Case 2: a < 0 If a is negative, then multiplying it with 2k (which is an even number) will give a negative result. This is what we need based on the given condition, so this case is possible. From the above analysis, we can conclude that n must be a negative even number for the inequality an < 0 to hold true.
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