Friday, February 27, 2009

Number Patterns

I have a problem taken from a primary five worksheet which I have been unable to solve. I need your advice: List three terms to continue a pattern in each of the following. 5, 6, 14, 32, 64, 115, 191, ...
Linda (Singapore), a parent of a primary five boy

Why don't you ask your child to try and listen to his reasons. There are different possible answers depend on the relationship that we give to the numbers. This is the case when the blanks are at the end. Although it is good discussion problem, as an examination item it needs to be less ambiguous.

My son managed to solve the problem for me.

List three terms to continue a pattern in each of the following. 5, 6, 14, 32, 64, 115, 191, 299, __, __

This is his explanation but I am not sure of it is correct. Please advise.

Find the difference between each of the above numbers:
1 8 18 32 51 76 108
Find the difference between these numbers again:
7 10 14 19 25 32
Find their difference again to get a common difference:
3 4 5 6 7
and continue again to get
1 1 1 1
So to find the next three terms, just add the numbers from 1 , e.g. 1 + 7 + 32 + 108 = 299 and then continue to find the next difference again.
Linda (Singapore), a parent of a primary five boy
You should congratulate your child. He has done a good job.