In each number except 383, the product of first and third digits is the middle one.
1, 1 + 12 = 2, 2 + 22 = 6, 6 + 32 = 15, 15 + 42 = 31, 31 + 52 = 56, 56 + 62 = 92
Last number of given series must be 92 not 91.
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8.
So, the next number is 8 x 9 = 72.
Each of the numbers except 28, is a multiple of 3.
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.
Go on multiplying the given numbers by 2, 3, 4, 5, 6.
So, the correct next number is 1440.
Alternatively 23 is added and 17 is subtracted from the terms. So, 634 is wrong.
The Sum of the digits in each number, Except 324 is 10.
The terms are alternatively multiplied by 1.5 and divided by 3. However, 18.5 does not satisfy it.
Subtract 1, 3, 5, 7, 9, 11 from successive numbers.
So, 34 is wrong.
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.
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