In a class of students, the first student has 2 toffees, second has 4 toffees. third has 6 toffees and so on. If the number of students in the class is 25. Then the total number of toffees are divisible by . . . . . .

Solution (By Examveda Team)

$$\eqalign{ & 2 + 4 + 6 + ...... \cr & {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right] \cr & = \frac{{25}}{2}\left[ {2 \times 2 + 24 \times 2} \right] \cr & = \frac{{25}}{2} \times 52 \cr & = 25 \times 26 \cr & {\text{Clearly it is divisible by }}5,\,13 \cr} $$