Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#7

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Question

A sequence  is defined by

, ,

Where  is a constant.

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

b)  Show that .

Given that ,

c)   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 required to find .

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

We can substitute  from (a);

c)    

We are given that;

It is evident that we sum of first 4 terms of given arithmetic sequence is 43.

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

We need to find 4th term.

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

We can substitute  from (a);

Therefore;

As per given condition;

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