CBSE Class 10 Answered

Let a be the first term and d be the common difference in arithmetic progression.

If sum S_m of m terms is n , then we have

  ......................(1)

From above expression, we get ,

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

If sum S_n of n terms is m , then we have

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

From above expression, we get

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

By subtracting eqn.(4) from eqn.(2) , we get

....................... (5)

Sum of (m+n) terms is

From eqn.(1) , we know that first term of above expression is n .

From eqn.(3) , we know that first term of above expression is m

Hence above expression becomes.

Using eqn.(5) , above expression is written as

Hence sum of (m+n) terms of arithmetic progression is -(m+n).

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