Find the next term in the sequence negative eight, 16, negative 24, 32, what.
In this sequence, we can see that there is a mixture of negative and positive values. When the signs in a sequence alternate between positive and negative, it’s called an alternating sequence. Sometimes the difficult thing about alternating sequences is finding the general or 𝑛th term. But we don’t need to do that here. We just need to find the next term in the sequence. So, let’s consider the absolute value of each term in the sequence.
When we write the absolute values, the sequence would be eight, 16, 24, 32, and so on. This sequence of absolute values would be an arithmetic sequence. That’s because there is a constant difference between any consecutive pair of terms. And so to find the next term in this sequence of absolute values, we would simply add eight. That would mean that the fifth term here would be 40.
But of course, the sequence that we were given is not simply the absolute values. So, we need to check if the value of 40 should stay as a positive value or if it should be negative 40. If we consider this sequence to have an index of 𝑛 greater than or equal to one, then the first term here would be negative eight. The third term is also negative. It’s negative 24. That means that any term in the sequence with an odd index must be negative. Therefore, we can give the answer that the next term in the sequence negative eight, 16, negative 24, 32 must be negative 40.