statement 1 taken separately gives you the general term x(i) for i>1, so there is no way to deduct x(1).

statement 2 separately gives us clues only about x(5). No way to solve it either.

Taken together, we have:

x(i)=x(i-1)/2
and
x(5)=x(4)/x(4)+1

From these statements, we can say that x(4)+1=2, x(4)=1

Using the general term x(i)=x(i-1)/2, we can say that x(1)=2*x(2)=2*2*x(3)=2*2*2*x(4)=2*2*2*1=8


So using the statements separately, no solving.

Statements together, we have a solution.

I am still confused on how both of them are sufficient.... Can you please help clarifying a little more.....Break it down so that I can really understand.....it is registering in my brain...

It is clear that neither alone is sufficient. So try to solve the problem using both statements.

the problem is to find x(1).

You have 2 statements:

x(i)=x(i-1)/2

x(5)=x(4)/x(4)+1.

Both statements are true.

So lets calculate x(5) based on the first statement:

x(5)=x(5-1)/2=x(4)/2 --------------------------------- (1)

but x(5) is also = x(4)/x(4)+1------------------------- (2)

Acording to (1) and (2), we have the following equation:

x(4)/2=x(4)/x(4)+1. Divide the equation by x(4).

1/2=1/x(4)+1

x(4)+1=2

x(4)=1.


So we know x(4).

From the first statement,
x4=x3/2 => x3=2*x4
x3=x2/2 => x2=2*x3=2*2*x4.
x2=x1/2 => x1=2*x2=2*2*2*x4.

x4=1, so x2=2*2*2*1=8.

So using both statements, we can solve this problem.

Hope i was clear enough, I'm not very good at explaining stuff.

I understand how to do the problem now....Had to kind of keep trying but finally understand your logic.....

Thanks....your the best....