According to the plan, 70 pounds of candy will be produced during the first week and the amount of candy produced during each week after the first will be 2 pounds greater than the amount produced during the preceding week. What will be the total amount of candy produced during the first 6 weeks?
The total amount of candy produced during the first 6 weeks will be 450 pounds.
The production of candy follows an arithmetic sequence where the first week produces 70 pounds and each subsequent week increases production by 2 pounds. By calculating the total production over the first six weeks, we find that the sum is 450 pounds.
This choice represents a value far below the actual total. The production starts at 70 pounds, and even without increases, the total would exceed 80 pounds just in the first week alone. Therefore, this option is not feasible.
While this option is closer than A, it still underestimates the total production. The total produced in just the first three weeks (70 + 72 + 74) already exceeds 140 pounds, indicating that the total over six weeks must be much higher.
This choice is a significant underestimate as well. The calculated amounts for each week add up to 450 pounds. Even without calculating explicitly, the increase in production each week leads to a total that far exceeds 420 pounds.
This choice accurately reflects the total production over the first six weeks, calculated as follows: 70 + 72 + 74 + 76 + 78 + 80 = 450. This total confirms the arithmetic progression of the candy production.
This option overestimates the total production. The highest weekly amount (80 pounds) in the sixth week does not compensate for the lower amounts produced in the prior weeks, making it impossible to reach 600 pounds in total.
The arithmetic sequence of candy production results in a total of 450 pounds produced over the first six weeks, with each week producing an increasing amount of 2 pounds more than the previous week. Calculating the total confirms choice D as the accurate answer, while all other options fail to reflect the correct total due to either underestimation or overestimation.
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