Mark M. answered • 09/09/18

Mathematics Teacher - NCLB Highly Qualified

Neal H.

asked • 09/09/18Help me this is too hard

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Mark M. answered • 09/09/18

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0 + 3 = 3

3 + 5 = 8

8 + 7 = 15

15 + 9 = 24

24 + 11 = 35

35 + 13 = 46

Make a difference table like this:

0

3

3 2

5

8 2

7

15 2

9

24 2

11

35

Notice that I have simpl extended the pattern in the table to produce the next number in the sequence, namely 35.

The 2nd column lists the difference between 2 successive numbers in the first column; this column is called the first difference. The 3rd column is the difference between 2 successive numbers in the 2nd column and is called the 2nd difference.

I cannot prove this for you now, but I can tell you that whenever you see a difference table like this with the 2nd difference column constant then the 1st difference will be an arithmetic sequence and the first column will be a quadratic sequence.

In this case the the difference column is given by 2n + 1 where n ≥ 1. The original sequence is given by n^{2} - 1

for n ≥ 1.

Doug C. answered • 09/09/18

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Hi Neal,

One technique to try is writing the difference between successive terms to see if a pattern develops. For example the difference between 3 and 0 is 3, the difference between 8 and 3 is 5, between 15 and 8, 7.

So we have 3, 5, 7... Checking one more difference gives 24-15 = 9. Looks like the difference between successive terms is the set of odd integers starting at 3. My guess is the next term will be 24+11 = 35.

Your question does not state how far out is required to "complete the sequence", but likely you get the idea. If you are required to state a rule for the nth term, then you are on to something a bit more complicated.

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