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There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p?
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There are five terms in the a.p the sum of these terms is 55and the fo...
Let the 5 terms be (a - 2d), (a - d), a , (a + d), (a + 2d)
Sum of all terms = 5a = 55
⇒ a = 11
4ᵗʰ term = 5 + (1ˢᵗ term + 2ⁿᵈ term)
⇒ a + d = 5 + a - 2d + a - d
⇒ 4d = 5 + a
⇒ d = 16/4 = 4
On substituting the values of a and d we get the terms as 3, 7, 11, 15, 19
Community Answer
There are five terms in the a.p the sum of these terms is 55and the fo...
Given information:
- There are five terms in the arithmetic progression (a.p).
- The sum of these terms is 55.
- The fourth term is five more than the sum of first two terms.
To find:
- The terms of the arithmetic progression.
Solution:
Let us assume that the first term of the arithmetic progression is 'a' and the common difference is 'd'. Then, we can write the terms of the a.p as:
a, a+d, a+2d, a+3d, a+4d
Using the given information, we can form two equations:
- Sum of the terms = 55
a + (a+d) + (a+2d) + (a+3d) + (a+4d) = 55
5a + 10d = 55
a + 2d = 11 ---- equation (1)
- Fourth term = sum of first two terms + 5
a+3d = (a + a+d) + 5
a+3d = 2a + d + 5
a + 2d = 5 ---- equation (2)
Solving equations (1) and (2), we get:
a = 2
d = 3
Therefore, the terms of the arithmetic progression are:
2, 5, 8, 11, 14
Verification:
- Sum of the terms = 2+5+8+11+14 = 40
- Fourth term = 11 = Sum of first two terms (2+5) + 5.
- There are five terms in the arithmetic progression (a.p).
- The sum of these terms is 55.
- The fourth term is five more than the sum of first two terms.
To find:
- The terms of the arithmetic progression.
Solution:
Let us assume that the first term of the arithmetic progression is 'a' and the common difference is 'd'. Then, we can write the terms of the a.p as:
a, a+d, a+2d, a+3d, a+4d
Using the given information, we can form two equations:
- Sum of the terms = 55
a + (a+d) + (a+2d) + (a+3d) + (a+4d) = 55
5a + 10d = 55
a + 2d = 11 ---- equation (1)
- Fourth term = sum of first two terms + 5
a+3d = (a + a+d) + 5
a+3d = 2a + d + 5
a + 2d = 5 ---- equation (2)
Solving equations (1) and (2), we get:
a = 2
d = 3
Therefore, the terms of the arithmetic progression are:
2, 5, 8, 11, 14
Verification:
- Sum of the terms = 2+5+8+11+14 = 40
- Fourth term = 11 = Sum of first two terms (2+5) + 5.
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There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p?
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There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p?.
There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are five terms in the a.p the sum of these terms is 55and the fourth term is five more than the sum of first two terms.find the terms of the a.p?.
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