Question

If the sum of m terms of an AP is the same as the sum of its n terms . Show that the sum of its (m+n) terms is zero.

Answer 1

plz mark brainliest...

Answer 2

 Let a be the first term and d be the common difference.
Then 
Sm = Sn
=> m/2 {2a + (m-1)d} = n/2 {2a + (n-1) d}
=>2am +m(m-1)d = 2an +n(n-1)d 
=>2a(m-n) + {m^2 - n^2 - m-n) }
=>(m-n) {2a +(m+n-1)d = 0
=>{2a+(m+n-1)}d = 0        [Since m-n not equal to 0]  ....(i)
Now,
Sm+n = m+n/2{2a+(m+n-1)}d 
           = m+n/2 *0           from ....(i)
           = 0       p.d