Twice the sum of consecutive numbers n and is 510.

Twice the sum of consecutive numbers n and is 510. 

One of the numbers is n  

The next consecutive number is (n + 1)  

so                                            2 • [ (n) + (n + 1) ]  =  510  

next just work it on out             2 • (2n + 1)  =  510  

                                                4n + 2  =  510  

                                                4n  =  508  

                                                  n  = 127   and   (n + 1) = 128 

the consecutive numbers are    127 and 128 

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Sequences of consecutive integers:
2  * [127  to 128] = 510
2  * [ 84  to 86]    = 510
2  * [ 49  to 53]    = 510
2  * [ 40  to 45]    = 510
2  * [ 21  to 30]    = 510
2  * [ 10  to 24]    = 510
2  * [ 7  to 23]      = 510