# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#5

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**Question**

A sequence of numbers is defined by

,

Where is a constant.

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

**b) **Show that

Given that

**c) **Find a range of values of c.

**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) **

We are given that;

We know that;

We need to find first

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

Therefore;

According to given condition;

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