If the sum of the first m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that (m + n) 
= (m + p) 
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Let a denotes first term and d common difference of the A.P. then a k , the k th term of the A.P.
a k = a + (k – 1) d ; a 1 + a 2 + a 3 +.... + a m = a m + 1 + a m + 2 + ....+ a m + n
2S m = S m + n ; 2 . 
[2a + (m – 1) d] = 
[2a + (m + n – 1) d]
= 
= 1 + 
⇒ 
= 
......(i)
similarly 
= 
......(ii)
divide (i) by (ii)
= 
. 
⇒ 
= 
⇒ 
= 
(m + n) 
= (m + p) 
Hence Proved
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