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In an AP if Sm=Sn and also m>n then find the value of S(m-n)

In an AP if Sm=Sn and also m>n then find the value of S(m-n)

Grade:10

1 Answers

Arun
25750 Points
6 years ago
First term = a , common difference = d
Sm = n
→m/2(2a  + (m-1)d) = n  …….(1)
Sn = m
→n/2(2a  + (n-1)d) = m   ……..(2)
Eq. (2) – (1)
2a(n-m) + d(n2-n-m2+m)=2m-n
n-m{2a + d(n+m-1)}=-2(n-m) …….(3)
2a + d(n+m-1) = -2
Now, Sm+n = m+n/2{2a+(m+n-1)d}
=-(m+n) (using eq. 3)
Regards
Aru (askIITians forum expert)

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