# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#5

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**Question**

A sequence is defined by

,

Where is a positive integer.

**a) **Write down an expression for in terms of k.

**b) **Show that

**c) **

** i. **Find in terms of k, I its simplest form.

** ii. **Show that is divisible by 6.

**Solution**

**a) **

We are given that sequence is defined by

We are required to find .

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

**b) **

We are required to find .

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

**c) **

** i.
**

We are required to find .

We need to find first .

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

Therefore;

** ii.
**

We have found that;

We are required to show that is divisible by 6 which means 6 must be a factor of .

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