Question

A sequence  satisfies

, ,

Given that ,

a)   Find the value of  and the value of .

b)  Evaluate .

Solution

a)    

We are given that sequence  is defined by

We are given that  and required to find .

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

Similarly, we can find .

b)   

We are required to find;

It is evident that we are required to find sum of first 4 terms.

We have already found 3^rd and 4^th terms and are given 2^nd terms in (a). We need to find 1^st term.

Hence;