Here is the definition based on GMAT Review
"The number -2,-1,0,1,2,3,4,5....are consecutive integers. Consecutive integers can be represented by n, n + 1, n+2, n+3... where n is an integer. The numbers 0,2,4,6,8,...are consecutive even integers, and 1,3,5,7,9...are consecutive odd integers. Consecutive even integers can be represented by 2n,2n+2, 2n+4...., and consecutive odd integers can be represent 2n+1, 2n+3, 2n+5.... where n is an integer.""
Hope this help