Here is the solution:

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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.
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