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# CBSE Class 10 Answered

if in an A.P. the sum of m terms equal to n and the sum of n terms is equal to m, then prove that the sum of (m+n) terms is -(m+n)
Asked by ananya_monica | 28 Sep, 2023, 07:07: PM
Let  a be the first term and d be the common difference of A.P.

Sum of m terms of  A.P

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

Similarly , sum of n terms of A.P

............................... (2)
By solving eqn.(1) and (2) , we get

................................... (3)
.........................(4)

Sum of (m+n) terms of A.P is

....................... (5)
By substituting initial value a from eqn.(4) and d from eqn.(3) , we get from eqn.(5) after simplification is

Above expression is simplified to

-------------------------------------

Answered by Thiyagarajan K | 28 Sep, 2023, 09:44: PM

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