use the formula a+(n-1)d. where a--- first term of the sequence, and d---- the common difference between the terms (succeeding number minus proceeding number).

It is a little hard to explain it without drawing... But the figure is like a star with 4 hands (this is where the 4n comes from), every time you count the number of squares on every hand you also count the square in the middle (the square that unites all the hands), so you have in fact counted it 3 times in addition, thus you need to subtract 3. And so the answer is 4n-3.

OK....you will need to have a basic knowledge of functions for this !!

We see that fig 1 has 1 square, fig 2 has 5 squares, fig 3 has 9 squares and so on. If you notice, you can see that in each successive figure, there is an increment of 4 squares (1 on each end of previous figure).

Let the figure no. be $n$ . Then, if you set up a function $f$ to find the area, the function $f$ is defined like this ---->

$f(n)=4(n-1)+1$

$\implies f(n)=4n-4+1$

$\implies \boxed{f(n)=4n-3}$ where $n=\text{ Figure no. }$ and $f(n)=\text{ Area of figure }n$