Question

A sequence  is defined by

  ,

Where  is a positive integer.

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

b)  Show that

Given that

c)   Find the possible values of a.

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)    

We are given that;

We have found in (b) that;

Therefore;

Now we have two options.