What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?
1 answer:
Since the sequence is arithmetic, we have an expression of the form:
Where,
a1: first term of the sequence
d: common difference
n: number of terms
We look for the common difference:
Then, setting values we have:
Then, the sum of the terms is:
Substituting values:
Answer:
the sum of the arithmetic sequence 8, 15, 22 is:
Sn = 2483
Where,
a1: first term of the sequence
d: common difference
n: number of terms
We look for the common difference:
Then, setting values we have:
Then, the sum of the terms is:
Substituting values:
Answer:
the sum of the arithmetic sequence 8, 15, 22 is:
Sn = 2483
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Answer:
The maximum possible area of the pasture is 26,450 feet square.
Step-by-step explanation:
Let us assume the width of the rectangular area = m ft
and the length of the area = k ft
Also assume: ( one side with k units IS NOT FENCED)
So, the total perimeter of the fencing is:
2 m + k = 460
or, k = 460 - 2m ........ (1)
Now, AREA OF THE RECTANGULAR PORTION = Length x Width = k x m
Put k = 460 - 2m
We get: A = m (460 - 2m)
or, A = 460 m - 2m²
We need to find the maximum for the parabolic function A = 460 m - 2m²
The function has a maximum value as the quotient in front of x^2 is negative: -2 < 0
A (max) = where a = -2, b = 460, c = 0
=
A max = 26,450 sq ft.
The maximum possible area of the pasture is 26,450 feet square.