Tag Archives: Number sequence

7 Comments

4KM and 4KJ have been looking at number sequences...

Number Sequences and Patterns

One student replied to a comment I wrote. The class had looked at the Fibonacci Sequence I had shared and were able to work out the next number in...

0, 1, 1, 2, 3, 5, 8, 13, 21, …

They worked out, for example,  8 came from adding the previous two numbers, i.e. 3 + 5. 13 came from adding 5 and 8. 21 came from 8 and 13. They worked out the next number would be...

13 + 21 = 34

I shared a much harder sequence of numbers I found. I think many adults might have a problem solving this one...

15, 29, 56, 108, 208, ___

Given a choice of four possible next numbers, which do you think comes next...

a) 386   (b) 400   (c)  416   (d) 438

I gave the answer as (b) 400

Why is this so?

Looking at the numbers, I first noticed each number was roughly double the previous...

15, 30, 60, 120, 240

I then looked at the difference between the doubling and the sequence number...

15, 30-1, 60-4, 120-12, 240-32

But how could we work out the pattern? The number we subtract changes. Here is the pattern...

15, 2 x 15 - 1 x 1, 4 x 15 - 2 x 2, 8 x 15 - 3 x 4, 16 x 15 - 4 x 8

Notice...

1)  the number to multiply the 15 doubles each time

2) the first number in the subtracted multiplication goes up one each time

3)  the second number in the subtracted multiplication doubles each time

Using these patterns, the next number in the series would use the equation...

32 x 15 - 5 x 16 = 480 - 80 = 400

If a student understands how I worked out the sequence, what number comes after 400? Leave your answer in the comments.

Is this a case of being as clear as mud? 🙂

Schools and students have permission to use this graphic for non-commercial, educational purposes.

If you know anyone keen on hard number sequences, here is a link to a few. It is a number sequence test. The above sequence is part of the test...

Number Sequence Test - Hard