Question Practice on sum of n terms

Questions on Sum of n terms in A.P.

If in an A.P.the sum of m terms is equal to n and the sum of n terms is equal to m then prove that the sum of (m+n) terms is -(m+n)

In an A.P.the sum of m terms of an AP is n and sum of n terms of AP is m,then prove that sum of (m+n) terms of AP is -(m+n)

If the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms.Then,find the ratio of the sum of the 2n terms to the sum of next 2n terms.

Show that the ratio of the sum of first n terms of a G.P. and the sum of (n+1)th term to (2n)th term is (1)/(r^(n)) .

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+1) to (2n) terms is (1)/(r^(n))

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