Question

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).

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Answer 1

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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).

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Let a be the first term and d be the common difference of the given A.P. Then,

⟹$S_{m} = n$

$\frac{m}{2} \:{ {{2a + (m - 1)d} = n}}$

$2am \: + m(m - 1)d = 2n$

and

⟹$S_{n}=m$

rest is in the pic