# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#3

**Question**

A sequence is defined by

,

,

Where k is a positive constant.

**a) **Write down expressions for and in terms of k, giving your answers in their simplest form.

Given that ,

**b) **Find an exact value for k.

**Solution**

**a. **

We are given that sequence is defined by

We are required to find and in terms of k.

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

We are given that ;

Similarly;

We have found that ;

**b. **

We are given that;

It is evident that sum of first 3 terms of given arithmetic sequence is 10.

We already have these terms in (a).

Therefore;

As per given condition ;

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