Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#5

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Question

A sequence  is defined by

  ,

Where  is a positive integer.

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

b)  Show that

c)    

                    i.       Find  in terms of k, I its simplest form.

                  ii.       Show that  is divisible by 6.

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;

c)    

                            i.
 

We are required to find .

We need to find first .

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

Therefore;

                          ii.
 

We have found that;

We are required to show that  is divisible by 6 which means 6 must be a factor of .

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