#### Spicy Sequence Patterns

##### Difficulty:

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A sequence is a set of numbers that are in order. To find the missing number or next number we first have to find a rule behind the sequence.

Example:

What is the next term in 7, 13, 29, 61, 115, 197, 313, 469?

This might look overwhelming to begin with but lets just break it down one step at a time.

How did it get from 7 to 13? 6 was added.

How did we get from 13 to 29? 16 was added.

How did we get from 29 to 61? 32 was added.

How did we get from 61 to 115? 54 was added.

So what is the relationship between 6, 16, 32 and 54?

We can see that the numbers increase by 10, 16, 22 and they are increasing by 6.

So lets test that out, lets add 28 to 54 and we get 82, then add 82 to 115 and we get 197 which is the next number in the sequence so it works. We can test every step in the sequence and it works for all.

So its a little bit like breaking a code but if we just take one step at a time we can crack it.