If the sum of first m terms of an A.P. is n and the sum of first n terms is m, then show that the sum of its first (m + n) terms is

- (m + n).

Asked by Topperlearning User | 22nd Sep, 2017, 08:40: AM

Expert Answer:

Given, sum of first m terms of an A.P. is n.

Also, sum of first n terms is m.

Subtracting (2) from (1),

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rightwards double arrow fraction numerator straight m plus straight n over denominator 2 end fraction open square brackets 2 straight a space plus open parentheses straight m space plus space straight n space minus space 1 close parentheses straight d close square brackets space equals space minus 2 cross times fraction numerator straight m plus straight n over denominator 2 end fraction equals space minus open parentheses straight m space plus space straight n close parentheses end style

 

Hence, the sum of its first (m + n) terms is -(m + n).

Answered by  | 22nd Sep, 2017, 10:40: AM

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