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If you are aiming for the top grades, you need to be able to tie together sequences with surds.

The good news is that surds only appear in one type of sequence: Geometric sequences.
 

What is special about a geometric sequence?

A Geometric sequence is one that has a common ratio. This is where the next term is generated by multiplying the previous term.

For example, the sequence 2, 4, 8, 16 is generated by multiplying by 2.

 

How to find the common ratio.

This is surprisingly easy, all you have to do is to divide one term by the previous term, this will always give the common ratio.

 

Example: Continue the sequence √3, 3, 3√3, 9

Step 1: Find the common ratio.

I'm going to pick the third and second terms for this (just because the numbers are nice - you can pick whichever ones you want) to find the common ratio

3√3 ÷ 3 = √3

So my common ratio is √3

Step 2: Continue the sequence.

I now just need to multiply the fourth term by √3 to get the fifth term - 9 x √3 = 9√3

Then I can multiply this fifth term by √3 to get the sixth term - 9√3 x √3 = 9 x 3 = 27

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