Question

A sequence  is defined by

 ,

Where  is a constant.

a)   Write down expressions for  and  in terms of k.

Find,

b)   in terms of k, giving your answer in its simplest form.

c)   .

Solution

a)    

We are given that sequence  is defined by

We are required to find  and .

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

Similarly;

b)   

We are required to find;

We can substitute given  and found  from (a);

c)    

We are required to find;