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

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 3rd and 4th
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;