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CBSE Class 10 Answered

If the sum of first p terms of an AP is q and the sum of first q terms is p.THen find the sum of first (p+q) terms.
Asked by neeraj | 21 Jan, 2016, 07:47: PM
answered-by-expert Expert Answer
Let space straight a space be space the space first space term space and space straight d space be space the space common space difference space the space AP apostrophe straight s. Then space sum space to space their space straight n space terms space is space given space by comma straight S subscript straight p space equals end subscript straight q straight p over 2 open curly brackets 2 straight a plus open parentheses straight p minus 1 close parentheses straight d close curly brackets equals straight q 2 ap plus straight p left parenthesis straight p minus 1 right parenthesis straight d equals 2 straight q................. left parenthesis straight i right parenthesis straight S subscript straight q space equals end subscript straight p straight q over 2 open curly brackets 2 straight a plus open parentheses straight q minus 1 close parentheses straight d close curly brackets equals straight p 2 aq plus straight q left parenthesis straight q minus 1 right parenthesis straight d equals 2 straight p................. left parenthesis ii right parenthesis Subtract space equation space left parenthesis ii right parenthesis space from space equation space left parenthesis straight i right parenthesis comma space we space get 2 straight a left parenthesis straight p minus straight q right parenthesis plus open curly brackets straight p left parenthesis straight p minus 1 right parenthesis minus straight q left parenthesis straight q minus 1 right parenthesis close curly brackets straight d equals 2 straight p minus 2 straight q 2 straight a plus left parenthesis straight p plus straight q minus 1 right parenthesis straight d equals negative 2........... left parenthesis iii right parenthesis straight S subscript straight p plus straight q equals end subscript fraction numerator straight p plus straight q over denominator 2 end fraction open curly brackets 2 straight a plus open parentheses straight p plus straight q minus 1 close parentheses straight d close curly brackets straight S subscript straight p plus straight q equals end subscript fraction numerator straight p plus straight q over denominator 2 end fraction open parentheses negative 2 close parentheses................... left parenthesis from space left parenthesis iii right parenthesis right parenthesis straight S subscript straight p plus straight q equals end subscript minus left parenthesis straight p plus straight q right parenthesis Ratio space of space 9 th space terms space is space 5 colon 7
Answered by Vijaykumar Wani | 22 Jan, 2016, 11:32: AM

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