Question

A sequence  is defined by

 , for 

Where  is a constant.

a)   Find an expression for  in terms of k.

Given that ,

b)  Find the two possible values 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 given that;

It is evident that sum of first 3 terms of given arithmetic sequence is 2.

We are already given first term and have found 2^nd term in (a) while we need to find 3^rd term.

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

We can substitute  from (a);

Therefore;

As per given condition ;

Now we have two options.