Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#3

Question

A sequence  is defined by

, for

Where  is a constant.

a)   Find an expression for  in terms of k.

Given that ,

b)  Find the value of k.

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 given that;

It is evident that sum of first 3 terms of given arithmetic sequence is 66.

We are already given first term and have found 2nd term in (a) while we need to find 3rd term.

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

We can substitute  from (a);

Therefore;

As per given condition ;