If pth term of a
a.p is q and qth term is p prove that p+q th teems is 0
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let first term of A.P is a
& common difference be d
then
a+(p-1)d=q...........(1)
& a+(q-1)d=p............(2)
(1)-(2)
pd-qd=q-p
or d(p-q)=q-p
or d=-1
Putting the value of d in (1)
a-p+1=q
or a=p+q-1
then (p+q) the term
a+(p+q-1)d
=(p+q-1)-(p+q-1)=0....(proved)
& common difference be d
then
a+(p-1)d=q...........(1)
& a+(q-1)d=p............(2)
(1)-(2)
pd-qd=q-p
or d(p-q)=q-p
or d=-1
Putting the value of d in (1)
a-p+1=q
or a=p+q-1
then (p+q) the term
a+(p+q-1)d
=(p+q-1)-(p+q-1)=0....(proved)
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