# CBSE Class 10 Answered

**If the sum of the first π terms of an AP is π and the sum of first π terms is π. Then, show that the sum of its first (π + π) terms is −(π + π).**

Asked by yosuraj1234 | 05 Mar, 2019, 03:16: 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 ) + [ (m

^{2}- n^{2}) - (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, 12:07: AM

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