SEARCH HOME
 Math Central Quandaries & Queries
 Subject: math Name: rose Who are you: Student find the next 3 terms of the sequence 2,3,9,23,48,87

I want to do a similar problem.

Find the next term in the sequence 0, 2, 8, 21, 44, 80

Once you see how to find the next term you should see how to find the terms after that. The method I am going to use is successive differences. Start by finding the the differences of successive terms.

2 - 0 = 2
8 - 2 = 6
21 - 8 = 13
and so on.

Write the differences under the sequence to get 2 rows

 0 2 8 21 44 80 2 6 13 23 36

I'm looking for a pattern and I don't see one so I am going to construct another row of differences.

6 - 2 = 4
13 - 6 = 7
and so on.

 0 2 8 21 44 80 2 6 13 23 36 4 7 10 13

Still no obvious pattern so try it again.

 0 2 8 21 44 80 2 6 13 23 36 4 7 10 13 3 3 3

Now I see it. The third row of differences are all 3s. Thus the next number in the third difference row is a 3.

 0 2 8 21 44 80 2 6 13 23 36 4 7 10 13 3 3 3 3

This means that the next number in the second difference row must be 16.

 0 2 8 21 44 80 2 6 13 23 36 4 7 10 13 16 3 3 3 3

Thus the next number in the first row of differences must be 52.

 0 2 8 21 44 80 2 6 13 23 36 52 4 7 10 13 16 3 3 3 3

So finally the next number in the sequence is 132.

 0 2 8 21 44 80 132 2 6 13 23 36 52 4 7 10 13 16 3 3 3 3

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.