CBSE Class 10 Answered
If the sum of first m terms of an A.P. is n and the sum of first n terms is m, then show that the sum of its first (m + n) terms is - (m + n).
Asked by d7016880266 | 20 Jan, 2023, 08:14: PM
Let a be the first term and d be the common difference in A.P.
Sum of first m terms of A.P. :-
( given )

Sum of first n terms of A.P. :-
( given )

Above expressions can be written as


Subtracting eqn.(2) from eqn.(1) , we get

Dividing above expression by (m-n) , we get

Let us multiply above expression by ' (m+n)/2 ' and rewrite after simplification as

LHS of above expression is sum of first (m+n) terms of given A.P. ( Q.E.D)
Answered by Thiyagarajan K | 21 Jan, 2023, 08:32: AM
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