Final answer:
The invalid for loop declaration is a. for ( int i = 99; i >= 0; i / 9 ), because 'i / 9' is just an expression that calculates a value and does not update the loop variable i.option a.
Step-by-step explanation:
The for loop declaration that is not valid among the given options is a. for ( int i = 99; i >= 0; i / 9 ). In Java, the third part of a for loop declaration is supposed to be an expression that updates the loop variable. In option a, i / 9 is an expression that calculates a value but does not update the loop variable i. It should be something like i -= 9 or i /= 9 if the goal is to decrease i by dividing it by 9 on each iteration. The other options b, c, and d are all valid for loop declarations as they provide an update expression for the loop variable.
The correct answer is option a. for ( int i = 99; i >= 0; i / 9 )
This loop declaration is not valid because the increment operation i / 9 does not change the value of i in each iteration. It will result in an infinite loop.
On the other hand, options b, c, and d are valid for loop declarations. In option b, i-- decrements the value of i by 1 in each iteration. In option c, i *= 2 multiplies the value of i by 2 in each iteration. And in option d, i += 7 adds 7 to the value of i in each iteration.