To work out a question like this, you can divide the number by 2 ( 62.5) and then look at the integers on either side ( 62 and 63 )
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There are no four consecutive whole numbers that add up to 35. The sum of two consecutive [whole] numbers is an even number plus an odd number which is an odd number. The sum of two consecutive numbers and the two next consecutive numbers is the sum of two odd numbers which is even, but 35 is odd, so no four consecutive whole numbers cannot add up to 35.
The consecutive numbers that have a sum of 257 are 128 and 129.
Consecutive whole numbers will have an odd sum. Consecutive odd numbers, or consecutive prime numbers, will be 29 and 31.
Two consecutive numbers (pressumably integers) will always add up to an odd number, so this has no solution. If you mean "two consecutive even numbers" or "two consecutive odd numbers", you should quickly be able to find a solution by trial-and-error.
The sum of consecutive integers will always be odd. Consecutive odd numbers will be even. 299 + 301 = 600