about necessary and sufficient condition, again Here I have a sentence picked up from a first year book:

The statement “if A then B” is equivalent to the statement “A is a sufficient condition for B” and to the statement “B is a necessary condition for A"

I understand the first part, but I cannot see how the statement “if A then B”
leads to the conclusion that “B is a necessary condition for A".
Is a sufficient condition always a necessary condition?
Hope anyone could help for some explanation and examples.
Thanks

Here's my understanding:
It means that $A$ necessarily entails $B$.   
The first statement tells you that it's enough to have $A$ to get $B$. But you could have $B$ without $A$.  
The second statement tells you that given $A$, you have to have $B$.
