Construct a difference table to predict the next term of the sequence -1,3,18,47,93,159,248

362

Step-by-step explanation:

-1,3,18,47,93,159,248

First difference (just do term minus previous term):

4, 15, 29, 46, 66 ,89

The first differences are not common.

Second difference (doing term minus previous term)

11,  14,  17, 20, 23

Third difference:

3 ,3 ,3, 3

So it is a cubic because the third differences are the same.

Anyways we don't have to find the explicit form of this sequence.  We just have to find the next term.

Let's go back through starting with second difference:

11 , 14, 17, 20, 23 , (25)

(25) would be next term here.

Let's go back to first difference:

4, 15, 29, 46, 66 ,89 , (89+25)

4, 15 ,29, 46, 66, 89 , (114)

Now let's go back to original sequence:

We want 114+248 to be the next term.

That equals 362.