The growth of the lily pad is in geometric progression, and it covers half the pond in 29 days.
In the question, we are given that the size of the lily pad doubles itself every day.
If we assume the size of the lily pad on the first day as a, then on the second day its size will be 2a, on the third day it will be 2(2a) = 4a, and on the fourth day, it will be 2(4a) = 8a, and so on.
This makes a geometric progression, with the first term as a, and the constant ratio as 2.
We are given that on the 30th day, the size of the lily pad, covers the entire pond.
The size on the 30th day can be shown as the 30th term of this geometric progression
Therefore, size of the pond = a(2)³⁰⁻¹ = a.2²⁹. {Using the formula, aₙ = arⁿ⁻¹, where aₙ is the n-th term, a is the first term, and r is the constant ratio}.
We are asked the day on which the pond is half covered.
The size of the pond in this case = (a.2²⁹)/2 = a.2²⁸.
The day can be calculated as follows:
a.2ⁿ⁻¹ = a.2²⁸,
or, 2ⁿ/2 = 2²⁸,
or, 2ⁿ = 2²⁹,
or, n = 29.
Thus, the lily pad covers half the pond on the 29th day.
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