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
 A: 
is a sufficient condition always a necessary condition?

The phrases do not apply to A and B directly, they are just two ways of describing the same relationship between A and B while emphasizing the role of one of the conditions in the implication. The phrase "A is a necessary/sufficient condition" has no meaning without reference to a second condition.
As for an example, being a square is a sufficiently strong condition to guarantee being a rectangle. On the other hand, it is absolutely necessary to be a rectangle if you have any hope of being a square.
This might help: "being a rectangle is necessary for being a square: if you're not a rectangle, you are not a square." This statement just says "not rectangle $\implies$ not square" which is just the contrapositive of "square $\implies$ rectangle."
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".

You can get this intuition by drawing a truth table for $A \rightarrow B$
$$\begin{array} {|c|}
\hline
A & B & A \to B \\ \hline
1 & 1 & 1\\ \hline
1 & 0 & 0\\ \hline
0 & 1 & 1 \\ \hline
0 & 0 & 1 \\ \hline
\end{array}$$
You will see that whenever $A$ is true, so is $B$, which essentially mirrors the intuitive idea of $B$ being necessary for $A$.
A: 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 $B$.
A: "A is sufficient for B" is $A\to B$.  Also stated as "If A then B". 
This means that the truth of A garantees the truth of B, although B might be true when A is not.
That is either A is false or B is true.

"B is necessary for A" is $B\leftarrow A$.
This means that A cannot be true when B is not, but that A may not be true when B is.
That is either A is false or B is true.

Ergo they are equivalent.  $$A\to B \quad\iff\quad B\leftarrow A$$
