The number of feet down the hallway where you go until you start to feel pain is 14 feet.
<h3>What is geometric progression GP?</h3>
A sort of sequence known as geometric progression (GP) is one in which each following phrase is created by multiplying every preceding term by such a fixed number, or "common ratio."
The general form of GP is
a, ar, ar², ar³ ... arⁿ⁻¹
where, a is the initial term.
r is the common ratio.
According to the question,
The initial term is; a = 2.
The common ratio r = 2.
The threshold value beyond which person start feeling pain is 127.
Thus, last term; arⁿ⁻¹ = 128 (1 feet beyond 127 person start feeling pain)
Last second value is arⁿ⁻².
As, the common ratio is same in GP.
Thus, arⁿ⁻¹ / arⁿ⁻² = ar/a
==> 128/arⁿ⁻² = r
==> 128/arⁿ⁻² = 2
==> 2×2ⁿ⁻² = 64
==> 2ⁿ⁻² = 32
==> n = 7
As, i step is of 2 feet, the total steps taken by the person is 2×7 = 14.
Therefore, the total number of steps beyond which person will feel pain is 14.
To know more about the geometric progression, here
brainly.com/question/15978376
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