Question

A sequence  is defined by

 ,

 ,

Where k is a positive constant.

a)   Write down expressions for  and  in terms of k, giving your answers in their simplest form.

Given that ,

b)  Find an exact value for k.

Solution

a.    

We are given that sequence  is defined by

We are required to find  and  in terms of k.

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

We are given that ;

Similarly;

We have found that ;

b.    

We are given that;

It is evident that sum of first 3 terms of given arithmetic sequence is 10.

We already have these terms in (a).

Therefore;

As per given condition ;