Answer:
46 logs on the 5th row.
Step-by-step explanation:
Number of logs on the nth row is
n = 50 - (n-1)
n = 51 - n (so on the first row we have 51 - 1 = 50 logs).
So on the 5th row we have 51 - 5 = 46 logs.
The given relation is an arithmetic progression, which can be solved using the recursive formula: aₙ = aₙ₋₁ + d.
The 5th row has 46 logs.
An arithmetic progression is a special series in which every number is the sum of a fixed number, called the constant difference, and the first term.
The first term of the arithmetic progression is taken as a₁.
The constant difference is taken as d.
The n-th term of an arithmetic progression is found using the explicit formula:
aₙ = a₁ + (n - 1)d.
The recursive formula of an arithmetic progression is:
aₙ = aₙ₋₁ + d.
In the question, we are informed that logs are stacked in a pile. The bottom row has 50 logs and the next bottom row has 49 logs. Each row has one less log than the row below it.
The number of rows represents an arithmetic progression, with the first term being the row in the bottom row having 50 logs, that is, a₁ = 50, and the constant difference, d = -1.
We are instructed to use the recursive formula. We know the recursive formula of an arithmetic progression is, aₙ = aₙ₋₁ + d.
a₁ = 50.
a₂ = a₁ + d = 50 + (-1) = 49.
a₃ = a₂ + d = 49 + (-1) = 48.
a₄ = a₃ + d = 48 + (-1) = 47.
a₅ = a₄ + d = 47 + (-1) = 46.
Hence, the 5th row will have 46 logs.
Learn more about arithmetic progressions at
https://brainly.com/question/7882626
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