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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

..............................(1)

.................... ..........(2)

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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