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If the sum of first p term of an AP is ap^2 bp, find common difference?
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If the sum of first p term of an AP is ap^2 bp, find common difference...
Given that the sum of p terms of an AP is ap²+ bp .
Now, Put p = 1,2,3,...
S 1 = a(1)² + b(1)
S1 = a + b = a 1
S2 = a(2)² + b(2)
S2 = 4a + 2b
Now, S2 = a1 + a 2
4a + 2b = a + b + a 2
4a + 2b - a - b = a 2
3a + b = a 2
Common difference, d = a2 - a1
d = 3a + b - (a + b)
d = 3a + b - a - b
d = 2a
Therefore, the common difference of the given AP is 2a.
Now, Put p = 1,2,3,...
S 1 = a(1)² + b(1)
S1 = a + b = a 1
S2 = a(2)² + b(2)
S2 = 4a + 2b
Now, S2 = a1 + a 2
4a + 2b = a + b + a 2
4a + 2b - a - b = a 2
3a + b = a 2
Common difference, d = a2 - a1
d = 3a + b - (a + b)
d = 3a + b - a - b
d = 2a
Therefore, the common difference of the given AP is 2a.
Community Answer
If the sum of first p term of an AP is ap^2 bp, find common difference...
Given, Sp = ap2 + bp
⇒ Sp = p(ap + b)
⇒ Sp = p(2b + 2ap)/2
⇒ Sp = p(2b + 2a(p - 1) + 2a)/2
⇒ Sp = p(2(a + b) + 2a(p - 1))/2
On comparing the above with Sn = n(2a + d(n - 1))/2 we get,
First term = a + b and Common difference, d = 2a
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If the sum of first p term of an AP is ap^2 bp, find common difference? 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 If the sum of first p term of an AP is ap^2 bp, find common difference? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of first p term of an AP is ap^2 bp, find common difference?.
If the sum of first p term of an AP is ap^2 bp, find common difference? 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 If the sum of first p term of an AP is ap^2 bp, find common difference? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of first p term of an AP is ap^2 bp, find common difference?.
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