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20. The first and last term of an AP are a and ,
respectively. If S is the sum of all the terms of the
AP and the common difference is k a ( )
a 2 2
,
,
− +
− , then
k is equal to
(a) S (b) 2S
(c) 3S (d) None of these?
respectively. If S is the sum of all the terms of the
AP and the common difference is k a ( )
a 2 2
,
,
− +
− , then
k is equal to
(a) S (b) 2S
(c) 3S (d) None of these?
Most Upvoted Answer
20. The first and last term of an AP are a and , respectively. If S is...
Explanation:
1. Identifying the terms of the AP:
Given that the first term of the AP is 'a' and the last term is 'a + 2k'. Therefore, the terms of the AP would be a, a+k, a+2k, ..., a + nk (where n is the number of terms in the AP).
2. Calculating the sum of the AP:
The sum of an AP can be calculated using the formula: S = n/2 * (first term + last term), where n is the number of terms. Substituting the values, we get:
S = n/2 * (a + a + nk)
S = n/2 * (2a + nk)
S = n * (a + nk/2)
3. Expressing k in terms of S:
Given that the common difference is k = a/2 - a, we can express k in terms of S:
k = a/2 - a
k = -a/2
Substitute this value of k in the formula for sum:
S = n * (a - a/2)
S = n * (a/2)
n = 2S/a
4. Substitute n in terms of S in the expression for sum:
S = 2S/a * (a + a(-a/2)/2)
S = 2S/a * (a - a^2/4)
S = 2S/a * (4a - a^2)/4
S = (8S - 2Sa)/4
4S = 8S - 2Sa
2Sa = 4S
k = 2
Therefore, the value of k is 2. The correct answer is (b) 2S.
1. Identifying the terms of the AP:
Given that the first term of the AP is 'a' and the last term is 'a + 2k'. Therefore, the terms of the AP would be a, a+k, a+2k, ..., a + nk (where n is the number of terms in the AP).
2. Calculating the sum of the AP:
The sum of an AP can be calculated using the formula: S = n/2 * (first term + last term), where n is the number of terms. Substituting the values, we get:
S = n/2 * (a + a + nk)
S = n/2 * (2a + nk)
S = n * (a + nk/2)
3. Expressing k in terms of S:
Given that the common difference is k = a/2 - a, we can express k in terms of S:
k = a/2 - a
k = -a/2
Substitute this value of k in the formula for sum:
S = n * (a - a/2)
S = n * (a/2)
n = 2S/a
4. Substitute n in terms of S in the expression for sum:
S = 2S/a * (a + a(-a/2)/2)
S = 2S/a * (a - a^2/4)
S = 2S/a * (4a - a^2)/4
S = (8S - 2Sa)/4
4S = 8S - 2Sa
2Sa = 4S
k = 2
Therefore, the value of k is 2. The correct answer is (b) 2S.
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20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these?
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20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these? 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 20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these?.
20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these? 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 20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these?.
Solutions for 20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these? in English & in Hindi are available as part of our courses for Class 10.
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20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these?, a detailed solution for 20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these? has been provided alongside types of 20. The first and last term of an AP are a and , respectively. If S is the sum of all the terms of the AP and the common difference is k a ( ) a 2 2 , , − + − , then k is equal to (a) S (b) 2S (c) 3S (d) None of these? theory, EduRev gives you an
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