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Home » The \(n\)-th term of an arithmetic sequence is: - Abbey Badges

The \(n\)-th term of an arithmetic sequence is: - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Round to 210.

📌 7: A robotics engineer designs a conveyor system where a sensor detects parts every 1.25 seconds. Each part requires 8.5 seconds of processing by a robotic gripper. How many parts are being processed simultaneously at any given time in steady state?

📌 Number of parts in process = time per part × processing time = \( 8.5 \times 1.25 = 10.625 \), rounded to nearest whole number is 11.

📌 But since partial processing isn't possible, and system aims to maintain throughput, we interpret as average number in cycle: \( \frac{8.5}{1.25} = 6.8 \), which suggests core processing time relationship.

📌 However, correct interpretation: if parts arrive every 1.25 s and take 8.5 s to process, then at any time, number of active parts = \( \frac{8.5}{1.25} = 6.8 \), but in steady state with continuous flow, the number in process is \( \text{arrival rate} \times \text{service time} = \frac{1}{1.25} \times 8.5 = 6.8 \). Since partial parts aren’t physical, but for modeling, we report as computed.

📌 But question asks for number being processed — expected based on queue logic: \( \frac{8.5}{1.25} = 6.8 \), but must be integer. However, in modeling, fractional is acceptable. But final answer expected as computed:

📌 \( 8.5 / 1.25 = 6.8 \), but since parts are discrete, use exact value. However, previous examples use exact math. So:

📌 \( 8.5 \div 1.25 = 6.8 \). But let’s re-express:

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