What will be the next number in the series ? 6, 15 , 28 , 45 , ??

Answer 1

Here is the solution:

The solution is based on, sum of n numbers ( n * (n +1) / 2) i.e  1 + 2 + 3 + 4 ..
In our case the sequence is 6, 15, 28, 45, ?
Its nothing but sum of (1+2+3,  1+2+3+4+5,  1+2+3+4+5+6+7) i.e sum of 3, 5 , 7, 9 ..

So apply the above.
3  * (3 + 1)  / 2 = 3 * 2 = 6
5  * (5 + 1)  / 2 = 5 * 3 = 15
7  * (7 + 1)  / 2 = 7 * 4 = 28
9  * (9 + 1)  / 2 = 9 * 5 = 45
11 * (11 + 1) / 2 = 11 * 6 = 66

So the ans is 66.