CBSE Class 10 Answered
If the sum of the first
Asked by yosuraj1234 | 05 Mar, 2019, 15:15: PM
Expert Answer
Let a and d are first term and common difference of Arithmetic progression
Given : sum of first m terms are n, Hence we have, (m/2)[ 2a + (m-1)d ] = n or 2am + m(m-1)d = 2n ..................(1)
Given : sum of first n terms are m, Hence we have, (n/2)[2a + (n-1)d ] = m or 2an + n(n-1) d = 2m ...................(2)
Eqn. (1) - Eqn.(2) gives, 2a ( m - n ) + [ (m2 - n2) - (m-n) ] d = 2 (n-m) ...........................(3)
dividing eqn.(30 by (m-n) on both sides, 2a + (m+n-1)d = -2 ..........................(4)
sum of first (m+n) terms = [ (m+n)/2 ] [2a + (m+n-1)d ] = [ (m+n)/2 ] (-2) = -(m+n) ..........................(5)
we used eqn.(4) in eqn.(5)
Answered by Thiyagarajan K | 06 Mar, 2019, 00:03: AM
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