A machine makes (500) items in the first hour and production decreases by (20) items each next hour. What is the production in the (14)th hour?

Correct answer: (240)

The direct answer is option A, 240 items. This is a decreasing arithmetic progression because the production changes by the same amount every hour. The first-hour production is a=500, and production decreases by 20, so the common difference is d=-20, not +20. The nth-term formula is a_n=a+(n-1)d. For the fourteenth hour, a_14=500+(14-1)(-20)=500+13(-20). First calculate 13×20=260; then 500-260=240. Thus the machine makes 240 items in the fourteenth hour. Option A, 240, matches the calculation. Option B, 260, would result from subtracting 12 groups of 20, which corresponds to the thirteenth hour, so it is one hour early. Option C, 280, corresponds to subtracting 11 groups and is even earlier. Option D, 300, corresponds to subtracting 10 groups and is not the fourteenth-hour value. The factor is 13, not 14, because the first hour already has the starting value 500; only the changes after the first hour are counted. In a decreasing AP, write d as negative. A quick check is to continue: hour 1 is 500, hour 2 is 480, and after thirteen decreases of 20 the answer is 240.