The distance between the first and the last tree is 132 feet.
What is an Arithmetic Progression?
An arithmetic progression(A.P.) is a series, where the difference between consecutive numbers is constant.
The first term of an A.P. is denoted by a, and the common difference is denoted by d.
The nth term of an A.P. series is found using the formula:
aₙ = a + (n-1)d.
The sum of n terms of an A.P. series is found using the formula:
Sₙ = (n/2)(2a + (n-1)d)
How do we solve the given question?
We are said that every tree is equally spaced. So the distance between the trees is in arithmetic progression.
With the first tree being at 0 feet from itself, our a = 0.
The distance from the first tree to the sixth tree is 60 feet, so we can say that the 6th term is 60
6th term = a + 5d
or, 60 = 0 + 5d
or, d = 60/5 = 12 feet.
To find the distance between the first tree and the last tree(12th tree), we will find the 12th term of the series,
12th term = a + (12-1)d = 0 + 11(12) = 132 feet.
∴ The distance in feet between the first and last tree is 132 feet.
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