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M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0?
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M times the mth term of an AP is equal to n times the nth term,then sh...
Let the first term of AP = a
common difference = d
We have to show that (m+n)th term is zero or a + (m+n-1)d = 0
mth term = a + (m-1)d
nth term = a + (n-1) d
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M times the mth term of an AP is equal to n times the nth term,then sh...
Proof that (m n)th term is 0 when M times the mth term equals n times the nth term:
- Let us consider an arithmetic progression (AP) with common difference d.
- The mth term of the AP is given by: a_m = a_1 + (m-1)d
- The nth term of the AP is given by: a_n = a_1 + (n-1)d
Given:
M times the mth term = n times the nth term
=> M(a_1 + (m-1)d) = n(a_1 + (n-1)d)
Expanding the above equation:
=> Ma_1 + M(m-1)d = na_1 + n(n-1)d
=> Ma_1 + Mmd - Md = na_1 + n^2d - nd
Rearranging the terms:
=> (Mm - n)n = (M - n)d
Since it is an AP, the common difference d is constant:
=> Mm - n = M - n
=> Mm = M
Therefore, (m n)th term is 0:
Since Mm = M, we have Mm - M = 0
Hence, the (m n)th term of the AP is 0.
- Let us consider an arithmetic progression (AP) with common difference d.
- The mth term of the AP is given by: a_m = a_1 + (m-1)d
- The nth term of the AP is given by: a_n = a_1 + (n-1)d
Given:
M times the mth term = n times the nth term
=> M(a_1 + (m-1)d) = n(a_1 + (n-1)d)
Expanding the above equation:
=> Ma_1 + M(m-1)d = na_1 + n(n-1)d
=> Ma_1 + Mmd - Md = na_1 + n^2d - nd
Rearranging the terms:
=> (Mm - n)n = (M - n)d
Since it is an AP, the common difference d is constant:
=> Mm - n = M - n
=> Mm = M
Therefore, (m n)th term is 0:
Since Mm = M, we have Mm - M = 0
Hence, the (m n)th term of the AP is 0.
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M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0?
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M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0? 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 M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0?.
M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0? 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 M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for M times the mth term of an AP is equal to n times the nth term,then show that (m n)th term is 0?.
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