Question

In an A.P, Sm = n and Sn = m ,also m > n ,find the sum of first ( m-n ) terms.

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Answer 1

Answer:

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Answer 2

Given; In an A.P, Sm = n and Sn = m, also m > n

To Find; the sum of the first ( m-n ) terms.

Solution; It is given that In an A.P, Sm = n and Sn = m, also m > n

Sn=n2[2a+(n−1)d] =m

Sm=m2[2a+(m−1)d]=n

Sn−Sm=n2[2a+(n−1)d]−m2[2a+(m−1)d]

2(m−n)=2a(n−m)+[(n2−m2)−(n−m)]d−2(n−m)=(n−m)[2a+{(n+m)−1}d]

Divide (n-m) to both sides.

−2=2a+{(n+m)−1}d

Sm+n=−(m+n)

Hence the sum is -(m+n)