Question

     i.       A sequence  is defined by

 ,

 and

Find the value of

a)    

b) 

   ii.       A sequence  is defined by

 ,

 and , where k is a constant

a)   Find  and  in terms of k.

Given that ,

b)  Find the value of k.

Solution

i.
 

a)    

We are given that sequence  is defined by

We are required to find  when  and .

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

We are given that  and ;

b)   

We are required to find the value of ;

It is evident that sum of first 20 terms of given arithmetic sequence is required.

We are already given first and second term and have 3^rd  term in (a).

It is evident all the terms in the sequence are 4s. Therefore, we need to add4 altogether 20 times; 

ii.
 

a.    

We are given that sequence  is defined by

 and

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  and ;

Similarly;

We are given and have found that  and ;

b.    

We are given that;

It is evident that sum of first 5 terms of given arithmetic sequence is 165.

We already have first 04 terms in (a) while we need to find 5^th term. 

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

We
are given and have found that  and ;

Therefore;

As per given condition ;