Explanation:

Given series 23,32,42,53,65,76
 32-23=9
 difference of second to 1st number
 42-32=10
 3rd number to 2nd number
 53-42=11
 4th number to 3rd number
 65-53=12
 5th number to 4th number
 76-65=11
 
 difference increases 9 ,10,11,12

 11 is removed,13 is coorect
 65+13=78
 odd number is 76