1, 1, 2, 6, 24, 96, 720

Let the given numbers be A, B, C, D, E, F, G.

Then, A, A x 1 + 1, B x 2 + 2, C x 3 + 3, D x 4 + 4, E x 5 + 5, F x 6 + 6 are the required numbers.

Clearly, 228 is wrong.

There are two series, beginning respectively with 3 and 7. In one 3 is added and in another 2 is subtracted.

The next number is 1 - 2 = -1.

Numbers are 1³, 2³, 3³, 4³, 5³, 6³.

So, the missing number is 7³ = 343.

Each number is double the preceding one plus 1.

So, the next number is (255 x 2) + 1 = 511.

Numbers are alternatively multiplied by 2 and increased by 3.

So, the missing number = 61 x 2 = 122.

Numbers must be (14)², (13)², (12)², (11)², (10)², (9)², (8)².

So, 80 is wrong.

Go on subtracting 3 and dividing the result by 2 to obtain the next number.

Clearly, 46 is wrong.

Go on subtracting 24, 21, 18, 15, 12, 9 from the numbers to get the next number.

190 - 24 = 166
166 - 21 = 145
145 - 18 = 127 [Here, 128 is placed instead of 127]
127 - 15 = 112
112 - 12 = 100 ... and so on.

Therefore, 128 is wrong.

Go on adding 7, 9, 11, 13, 15, 17 respectively to obtain the next number.

So, 33 is wrong. It must be 35

A x 2 + 1, B x 3 + 1, C x 2 + 1, D x 3 + 1 and so on.

So, 356 is wrong.