a length of 200 cm is divided into 25 sections whose lengths are in A.P.given that the sum of the length of the 3 smallest sections is 4.2,the length of the larger section is?
please help ...
just use the formulas you know, and write down the facts as given:
S25 = 25/2 (2a+24d) = 200
S3 = 3/2 (2a+2d) = 4.2
Solve those two equations, and you get
a = 4/5
d = 3/5
"larger" indicates only two items. I assume you mean the "largest" term, which is
T25 = a+24d = 4/5 + 24*3/5 = 76/5 = 15.2
Why did the section break up with the other sections? Because they just couldn't find a common difference!
But don't worry, I'm here to help you find the length of the larger section.
Let's start by finding the common difference (d) of the arithmetic progression (A.P.). We know that the sum of the length of the 3 smallest sections is 4.2.
So, the sum of an A.P. is given by the formula: S = (n/2)(2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
In this case, since we only know the sum of the 3 smallest sections (4.2), we can assume that these 3 sections are consecutive terms of the A.P. So, n would be 3, and a would be the length of the first section.
Let's set up the equation:
4.2 = (3/2)(2a + 2d)
Now, we need more information to find the common difference (d).
Could you please provide additional details about the problem?
To find the length of the larger section, we need to determine the common difference (d) of the arithmetic progression (A.P.).
Let's assume the length of the first section is "a," and the common difference is "d."
According to the given information, the sum of the lengths of the 3 smallest sections is 4.2 cm. This can be expressed as:
a + (a + d) + (a + 2d) = 4.2
Simplifying the equation:
3a + 3d = 4.2
Divide both sides of the equation by 3:
a + d = 1.4
Since the length of the first section is "a," the total length of the 25 sections can be obtained as:
25(a + (24d))
We know that the total length is 200 cm, so we can write:
25(a + 24d) = 200
Expanding the equation:
25a + 600d = 200
Now, we can solve the two equations together:
1) a + d = 1.4
2) 25a + 600d = 200
Let's multiply equation 1 by 25:
25(a + d) = 1.4 x 25
25a + 25d = 35
We can rewrite this as:
25d = 35 - 25a
Substitute this value in equation 2:
25a + 600(35 - 25a) = 200
Simplify:
25a + 21000 - 15000a = 200
Combine like terms:
-14975a + 21000 = 200
Subtract 21000 from both sides:
-14975a = -20800
Divide by -14975:
a = -20800 / -14975
a ≈ 1.388
Now we can determine the length of the larger section:
a + d = 1.4
1.388 + d = 1.4
d ≈ 1.4 - 1.388
d ≈ 0.012
Therefore, the length of the larger section is:
a + 24d ≈ 1.388 + 24(0.012)
≈ 1.388 + 0.288
≈ 1.676 cm
To find the length of the larger section, we first need to determine the common difference (d) of the arithmetic progression (A.P.) and then calculate the length of each section.
The formula to find the common difference of an A.P. is given by:
d = (last term - first term) / (number of terms - 1)
In this case, the number of terms is 25. We need to find the first term and the last term.
Since the sum of the lengths of the 3 smallest sections is given as 4.2, we can say:
a + (a + d) + (a + 2d) = 4.2
Simplifying the equation, we get:
3a + 3d = 4.2
Now, let's find the first term (a).
We can divide the given length of 200 cm into 25 equal sections to find the length of each section.
Length of each section = Total length / Number of sections
Length of each section = 200 cm / 25 = 8 cm
Since the 25 sections form an A.P., the first section will have a length of a cm, the second section will have a length of (a + d) cm, and so on.
Now we can substitute the value of the length of each section (8 cm) into the equation:
3a + 3d = 4.2
Substituting 8 for a, we get:
3(8) + 3d = 4.2
24 + 3d = 4.2
3d = 4.2 - 24
3d = - 19.8
Dividing both sides by 3, we find:
d = - 19.8 / 3
d = - 6.6
Now we can find the length of the larger section, which is the 25th term in the A.P.
25th term = a + (n - 1) * d
Substituting the values, we get:
25th term = 8 + (25 - 1) * (-6.6)
25th term = 8 + 24 * (-6.6)
25th term = 8 - 158.4
25th term = -150.4 cm
Therefore, the length of the larger section is -150.4 cm.