If the p th term of an A.P. is q and qth term is p,prove that the r th term is p+q-r. Which term of the series is zero.
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Answer:
Step-by-step explanation:
In A.P., nth term is a+(n-1)d
a+(p-1)d=q ->(1)
a+(q-1)d=p ->(2)
(1)-(2)
a+pd-d-a-qd+d=q-p
pd-qd=-(p-q)
d=-1
a-p+1=q
a=q-1+p
substitute a and d in below equation
a+(r-1)d
p+q-1-r+1
P+q-r
Hence proved!
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