Request a call back

If the sum of the first n terms of an AP be n and the sum of first n terms be m then sum of its (m+n) terms is -(m+n)
Asked by keshavsinghalhapur | 16 Jan, 2024, 08:46: PM

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

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

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

From above expression, we get ,

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

If sum Sn 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).

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

Answered by Thiyagarajan K | 16 Jan, 2024, 11:42: PM

## Concept Videos

CBSE 10 - Maths
Asked by deepikaselvam2009 | 20 Feb, 2024, 08:57: PM
CBSE 10 - Maths
Asked by keshavsinghalhapur | 16 Jan, 2024, 08:46: PM
CBSE 10 - Maths
Asked by keshavsinghalhapur | 15 Jan, 2024, 10:56: AM
CBSE 10 - Maths
Asked by skandachiranjeevin | 06 Dec, 2023, 07:08: PM
CBSE 10 - Maths
Asked by prassanna.j | 13 Nov, 2023, 11:24: PM
CBSE 10 - Maths