# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#5

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**Question**

A sequence of numbers is defined by

, for

Given that ,

.**a) **Find the value of .

**b) **Find the value .

**Solution**

**a. **

We are given that sequence is defined by

We are required to find when .

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

We are given that ;

**b. **

We are required to find the value of .

It is evident that sum of first 4 terms of given arithmetic sequence is required.

We are already given second term and have found first term in (a) while we need to find 3^{rd} and 4^{th }

terms.

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

We can substitute from (a);

Similarly;

We can substitute from (a);

Therefore;

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