# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#4

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**Question**

** i. **A sequence is defined by

,

and

Find the value of

**a) **

**b) **

** ii. **A sequence is defined by

,

and , where k is a constant

**a) **Find and in terms of k.

Given that ,

**b) **Find the value of k.

**Solution**

i.

**a) **

We are given that sequence is defined by

We are required to find when and .

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

We are given that and ;

**b) **

We are required to find the value of ;

It is evident that sum of first 20 terms of given arithmetic sequence is required.

We are already given first and second term and have 3^{rd} term in (a).

It is evident all the terms in the sequence are 4s. Therefore, we need to add4 altogether 20 times;

ii.

**a. **

We are given that sequence is defined by

and

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 and ;

Similarly;

We are given and have found that and ;

**b. **

We are given that;

It is evident that sum of first 5 terms of given arithmetic sequence is 165.

We already have first 04 terms in (a) while we need to find 5^{th} term.

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

We

are given and have found that and ;

Therefore;

As per given condition ;

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