Use a difference table to predict the next term in the sequence.9, 4, 3, 12, 37, 84, ___

Sure, let's use a difference table to predict the next term in the sequence.

The sequence is: 9, 4, 3, 12, 37, 84

First, let's find the first difference by subtracting each term from the next one:

4 - 9 = -5 3 - 4 = -1 12 - 3 = 9 37 - 12 = 25 84 - 37 = 47

So, the first difference sequence is: -5, -1, 9, 25, 47

Next, let's find the second difference by subtracting each term of the first difference from the next one:

-1 - (-5) = 4 9 - (-1) = 10 25 - 9 = 16 47 - 25 = 22

So, the second difference sequence is: 4, 10, 16, 22

We can see that the second difference sequence is not constant, so let's find the third difference:

10 - 4 = 6 16 - 10 = 6 22 - 16 = 6

So, the third difference sequence is: 6, 6, 6

Now, we can see that the third difference sequence is constant. This means that the original sequence is a cubic sequence.

To find the next term in the original sequence, we need to add the next term in each of the difference sequences to the last term in the original sequence:

The next term in the third difference sequence is 6 (since it's constant). The next term in the second difference sequence is 22 (last term) + 6 (from the third difference) = 28 The next term in the first difference sequence is 47 (last term) + 28 (from the second difference) = 75 The next term in the original sequence is 84 (last term) + 75 (from the first difference) = 159

So, the next term in the sequence is 159.