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CBSE Class 10 Answered

If the pth , qth and rth terms of an AP is a,b,c respectively , then show that :
a(q-r)+b(r-p)+c(p-q)=0
Asked by amoghknightoo7 | 11 Mar, 2016, 11:19: AM
answered-by-expert Expert Answer
begin mathsize 12px style Let space straight A thin space be space the space first space erm space and space straight D space be space the space common space difference space of space the space given space straight A. straight P. Then comma straight a equals pth space term rightwards double arrow straight a equals straight A plus left parenthesis straight p minus 1 right parenthesis straight D straight b equals qth space term rightwards double arrow straight b equals straight A plus left parenthesis straight q minus 1 right parenthesis straight D straight c equals rth space term rightwards double arrow straight c equals straight A plus left parenthesis straight r minus 1 right parenthesis straight D We space have comma straight a left parenthesis straight q minus straight r right parenthesis plus straight b left parenthesis straight r minus straight p right parenthesis plus straight c left parenthesis straight p minus straight q right parenthesis equals left square bracket straight A plus left parenthesis straight p minus 1 right parenthesis straight D right square bracket left parenthesis straight q minus straight r right parenthesis plus left square bracket straight A plus left parenthesis straight q minus 1 right parenthesis straight D right square bracket left parenthesis straight r minus straight p right parenthesis plus left square bracket straight A plus left parenthesis straight r minus 1 right parenthesis straight D right square bracket left parenthesis straight p minus straight q right parenthesis equals straight A left square bracket left parenthesis straight q minus straight r right parenthesis plus left parenthesis straight r minus straight p right parenthesis plus left parenthesis straight p minus straight q right parenthesis right square bracket plus straight D left square bracket left parenthesis straight p minus 1 right parenthesis left parenthesis straight q minus straight r right parenthesis plus left parenthesis straight q minus 1 right parenthesis left parenthesis straight r minus straight p right parenthesis plus left parenthesis straight r minus 1 right parenthesis left parenthesis straight p minus straight q right parenthesis right square bracket equals straight A cross times 0 plus straight D left square bracket straight p left parenthesis straight q minus straight r right parenthesis plus straight q left parenthesis straight r minus straight p right parenthesis plus straight r left parenthesis straight p minus straight q right parenthesis minus left parenthesis straight q minus straight r right parenthesis minus left parenthesis straight r minus straight p right parenthesis minus left parenthesis straight p minus straight q right parenthesis right square bracket equals 0 plus straight D cross times 0 equals 0 end style
Answered by Rashmi Khot | 11 Mar, 2016, 12:41: PM
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