Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

If the sum of the first π‘š terms of an AP is 𝑛 and the sum of first 𝑛 terms is π‘š. Then, show that the sum of its first (π‘š + 𝑛) terms is −(π‘š + 𝑛).
Asked by yosuraj1234 | 05 Mar, 2019, 03:15: PM
answered-by-expert 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, 12:03: AM
CBSE 10 - Maths
Asked by rrajansinghakb199 | 08 Apr, 2024, 05:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by nagalaxmidurgarao937 | 08 Apr, 2024, 01:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by sonawnerohan01 | 23 Mar, 2024, 12:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by pathakvaishnavi9139 | 23 Mar, 2024, 10:45: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by choudharyniki001 | 22 Mar, 2024, 08:49: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by vn3950372 | 18 Mar, 2024, 08:38: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
Γ—