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📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 A robotics engineer in NYC is testing a robotic arm that adjusts its grip strength based on sensor feedback. The arm applies 12 Newtons of force at the first attempt, and each subsequent attempt increases the force by 15% of the previous increase, starting with a proportional jump. If the initial force build-up is modeled as a geometric sequence, what is the total force applied after 6 attempts?

📌 The force increase follows a geometric pattern: first force = 12 N.

📌 The increments themselves form a geometric sequence: increase after 1st = 12*r, but since the force grows multiplicatively by 15% more than the last jump, the total force is a geometric series with initial term a = 12 and common ratio r = 1.15 (each new force is previous + 15% of the *amount* of increase — but since the problem states "increases by 15% of the previous increase", and assuming multiplicative effect on total, we model total finite model as a geometric series with a = 12, r = 1.15, n = 6.

📌 Total force = a(r^n - 1)/(r - 1) = 12(1.15^6 - 1)/(0.15)

📌 1.15^6 ≈ 2.313

📌 So, (2.313 - 1)/0.15 = 1.313/0.15 ≈ 8.7533

📌 Then, 12 × 8.7533 ≈ 105.04

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