The sum of even numbers between 1 and 31 is:

Let S_n = (2 + 4 + 6 + ..... + 30). This is an A.P. in which a = 2, d = 2 and l = 30
Let the number of terms be n Then,
a + (n - 1)d = 30
? 2 + (n - 1) x 2 = 30
? n = 15
$$\eqalign{ & \therefore {S_n} = \frac{n}{2}\left( {a + I} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{15}}{2} \times \left( {2 + 30} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 15 \times 16 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 240 \cr} $$