What number should appear next in this sequence? 309 ; 416 ; 525 ; 636 ; ?

Answer 1

Last 2 digits are square of 1st digits.
Hence 749

Answer 2

Based upon pattern recognition or simply adding 111+2 = 113 and then adding that to the last number in the series 636 = the answer of: 749

Comments

Interesting (as Spock would say), how different solutions can arrive at the same answer.
Or (from the 12th century French theologian Alain deLille), "Mille viae ducunt homines per saecula Romam."

Answer 3

It follows the logic below
309 + 107 = 416
416 + 109 = 525
525 + 111 = 636
636 + 113 = 749
The answer is 749

Answer 4

309
416
525
636
Square of first digit is next two digits
So ans is 749