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

## 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...