Question 6

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In the mark scheme it seems to make a jump from $ q\beta + r - p \beta^{2} =0 $ to $ (q-1)\beta + r - p \beta^{2} =0 $ and I can't for the life of me figure out where this extra $\beta$ term has come from. I know it's not a mistake because with my working I don't reach the final answer.

More specifically I am talking about Q6, (ii) in this document:

https://drive.google.com/file/d/0B6CGjKYdIeFEMG1OTjBNSmFTRlE/view

Do you mean the equation

Do you mean the equation right after the first A1 mark? If so, the extra beta comes from the other side of the equality sign (the left hand side of the equality is alpha u_{n+1} + beta ).