Question

if the sum m terms of an A.P. is the same as the sum of n terms, then what is the sum of m+n terms?

Answer 1

Step-by-step explanation:

Ans is zerom/2 * (2a + (m-1)d) = n/2 * (2a + (n-1)d)

cutting 2

we get

m(2a + (m-1)d) - n(2a+ (n-1)d) = 0

2am + m^2d - md -2an -n^2d +nd =0

2a(m-n) + (m^2 - n^2)d -(m - n)d =0

2a(m-n) + ( (m + n) (m- n) ) d - (m - n )d = 0

taking (m-n) common

2a + ( m + n -1) d = 0------------ 1

S m+n = m+n/2( 2a + (m+n -1)d

we know that 2a + (m+n)d is 0 from eqn. 1

therefore S m+n = 0

Answer 2

Answer:

If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.