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# The ratio of the sums of m and n terms of an A.P. is m^2(m square):n^2(n square). S.T. the ratio of the mth and nth terms is (2m-1):2n-1).

Asked by 26th January 2014, 7:19 AM
The sum of m terms of an A.P is am + m(m-1)d/2. That is we have, Sum of m terms = am + m^2(d/2) - (md/2) The sum of n terms of an A.P is an + n(n-1)d/2. That is we have, Sum of n terms = an + n^2(d/2) - (nd/2) Given that, Sum of m terms:Sum of n terms = = [am + m^2(d/2) - (md/2)] : [an + n^2(d/2) - (nd/2)] = m^2:n^2 That is we have, [2a+(m-1)d]:[2a+(m-1)d] = m:n That is, 2a(n-m)=d[(n-1)m-(m-1)n] That is, 2a(n-m)=d(n-m) That is, d = 2a Now, mth term:nth term=[a+(m-1)d]:[a+(n-1)d] That is, mth term:nth term=[a+(m-1)2a]:[a+(n-1)2a] That is, mth term:nth term=(2m-1):(2n-1)
Answered by Expert 29th January 2014, 4:38 PM
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