SSAT Math Question 352: Answer and Explanation

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Question: 352

11. Rohan begins a weight-lifting regimen by bench-pressing 25 pounds the first week, 30 pounds the second week, and 35 pounds the third week. If he keeps increasing the weight each week by the same amount, on what week in his weight-lifting regimen will Rohan bench press 65 pounds?

  • A. Week 6
  • B. Week 7
  • C. Week 8
  • D. Week 9

Correct Answer: D

Explanation:

The answer is D

The value of the nth term, Sn of an arithmetic sequence is given by the equation Sn = S1 + d(n - 1), where S1 is the first term of the sequence and d is the common difference between the terms. Here, the difference between terms is 5, the first term is 25, and the final term is 65. Use these numbers in an equation: 65 = 25 + 5(n - 1). Distribute 5: 65 = 25 + 5n - 5. Combine like terms and divide by 5: n = 9.

You can quickly write out the weights, by week, up to 65, and count the weeks: {25, 30, 35, 40, 45, 50, 55, 60, 65} contains nine terms.

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