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ICSE Class 10 Answered

If sum of m terms of an AP is n and sum of n terms of an AP is m, show that the sum of (m+n) terms of the AP is -(m+n)
Asked by Ananya | 19 Feb, 2018, 15:52: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight S subscript straight m equals straight n straight m over 2 open square brackets 2 straight a plus open parentheses straight m minus 1 close parentheses straight d close square brackets equals straight n On space simplifying space we space get 2 am plus straight m open parentheses straight m minus 1 close parentheses straight d minus 2 straight n equals 0........... left parenthesis straight i right parenthesis Similarly space for space straight S subscript straight n equals straight m rightwards double arrow 2 an plus straight n open parentheses straight n minus 1 close parentheses straight d minus 2 straight m equals 0......... left parenthesis ii right parenthesis Solving space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis straight d equals fraction numerator negative 2 open parentheses straight m plus straight n close parentheses over denominator mn end fraction space and space straight a equals fraction numerator left parenthesis straight n minus 1 right parenthesis left parenthesis straight m plus straight n right parenthesis minus straight m squared over denominator mn end fraction Find space straight S subscript straight m plus straight n space end subscript space using space values space of space straight a space and space straight d. you space will space get space straight S subscript straight m plus straight n space end subscript equals negative left parenthesis straight m plus straight n right parenthesis end style
Answered by Sneha shidid | 19 Feb, 2018, 16:33: PM

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ICSE 10 - Maths
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