# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#8

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**Question**

A sequence is defined by

, ,

Where is a positive integer.

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

**b) **Show that .

**c) **

** i. **Find in terms of k.

** ii. **Show that is divisible by 10.

**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;

We can substitute from (a);

**c) **

We are required to find .

It is evident that we need to find sum of first 4 terms of given arithmetic sequence.

We are already given first term and have found 2^{nd} and 3^{rd} terms in (a) and (b).

We need to find 4^{th} term.

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

We can substitute from (a);

Therefore;

**d) **

We are required to show that is divisible by 10.

We have found in (c) that;

It is evident that since has a factor 10, therefore, it is divisible by 10.

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