## Exam-Style Question on Iteration## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 158. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

(a) A sequence is defined by the following rule where \(u_n\) is the \(n^{th}\) term of the sequence:

$$u_{n+1}=u_n^2-5u_n+21$$If \(u_1=3\) find \(u_2\) and \(u_3\).

(b) A different sequence is defined by the following rule:

$$u_{n+1}=u_n^2-8u_n+17$$If \(u_1=5\) find \(u_2\) and \(u_3\) and \(u_{50}\).

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