# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#5

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**Question**

A sequence of positive numbers is defined by

,

**a) **Find and , leaving your answers in surd form.

**b) **Show that .

**Solution**

**a)
**

We are given that sequence is defined by

,

We are required to find and .

We can utilize the given expression for general terms beyond first term as;

Similarly;

**b)
**

We are required to find .

We can utilize the given expression for general terms beyond first term as;

Therefore, we first need to find ;

Hence;

We are given that sequence of positive numbers is desired;

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