Final answer:
The final value of 'x' displayed by the program will be -12, as the variable 'x' undergoes a series of additions and sign changes through nested loops.
Step-by-step explanation:
The code given represents an algorithm that updates the value of the variable 'x' through a series of nested loops. The first 'REPEAT' block instructs the program to repeat the inner set of commands 'a' times, which is 3 times in this case. Inside the first repeat block, there is another 'REPEAT' block that executes 'k' times, where 'k' equals 4.
Within this innermost loop, 'x' is incremented by 'a' each time, summing up to 'x + a * k' after the inner loop completes once. Since 'a' is 3 and 'k' is 4, the increase would be by 12. However, at the end of the inner loop, 'x' is then multiplied by -1, changing its sign.
Let's consider the changes to 'x' step by step:
During the first iteration of both loops, 'x' will go from 0 to 12 and then get multiplied by -1, resulting in 'x' being -12.
With each outer loop iteration, this process repeats, essentially multiplying the accumulated value of 'x' by -1 after each round of addition, creating a sign flip each time.
After all three iterations, the final value of 'x' will be the result of -12 (from the first iteration) flipping sign two more times.
Thus, 'x' will end up as a positive number. Calculating the iterations:
First iteration: x = 0 + 3*4 = 12; x = 12 * (-1) = -12
Second iteration: x = -12 + 3*4 = 0; x = 0 * (-1) = 0
Third iteration: x = 0 + 3*4 = 12; x = 12 * (-1) = -12
However, due to an error, the sign flips are not accounted for resulting in -12 after three iterations.
The final value of 'x' that will be displayed is -12.