WEBVTT
00:00:01.850 --> 00:00:09.340
Find the next term in the sequence negative eight, 16, negative 24, 32, what.
00:00:10.190 --> 00:00:15.420
In this sequence, we can see that there is a mixture of negative and positive values.
00:00:15.850 --> 00:00:22.200
When the signs in a sequence alternate between positive and negative, it’s called an alternating sequence.
00:00:22.920 --> 00:00:28.680
Sometimes the difficult thing about alternating sequences is finding the general or 𝑛th term.
00:00:28.910 --> 00:00:31.030
But we don’t need to do that here.
00:00:31.240 --> 00:00:34.530
We just need to find the next term in the sequence.
00:00:35.050 --> 00:00:39.620
So, let’s consider the absolute value of each term in the sequence.
00:00:40.000 --> 00:00:46.970
When we write the absolute values, the sequence would be eight, 16, 24, 32, and so on.
00:00:47.280 --> 00:00:51.440
This sequence of absolute values would be an arithmetic sequence.
00:00:51.710 --> 00:00:56.770
That’s because there is a constant difference between any consecutive pair of terms.
00:00:57.170 --> 00:01:03.220
And so to find the next term in this sequence of absolute values, we would simply add eight.
00:01:03.580 --> 00:01:06.710
That would mean that the fifth term here would be 40.
00:01:07.120 --> 00:01:11.840
But of course, the sequence that we were given is not simply the absolute values.
00:01:12.220 --> 00:01:19.560
So, we need to check if the value of 40 should stay as a positive value or if it should be negative 40.
00:01:19.930 --> 00:01:27.550
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.
00:01:27.920 --> 00:01:30.460
The third term is also negative.
00:01:30.500 --> 00:01:32.170
It’s negative 24.
00:01:32.390 --> 00:01:38.080
That means that any term in the sequence with an odd index must be negative.
00:01:38.510 --> 00:01:47.980
Therefore, we can give the answer that the next term in the sequence negative eight, 16, negative 24, 32 must be negative 40.