If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.
Given that the p th term of an A.P is q aand q th term is p.
We are required to find the (p+q) th term of that A.P.
Arithmetic progression is a sequence in which all the terms have common difference between them.
N th term of an A.P.=a+(n-1)d
p th term=a+(p-1)d
q=a+(p-1)d-------1
q th term=a+(q-1)d
p=a+(q-1)d---------2
Subtract equation 2 by 1.
q-p==a+(p-1)d-a-(q-1)d
q-p=pd-qd-d+d
q-p=d(p-q)
d=(p-q)/(q-p)
d=-(p-q)/(p-q)
d=-1
Put the value of d in 1.
q=a+(p-1)(-1)
q=a-p+1
a=q+p-1
(p+q) th term=a+(n-1)d
=q+p-1+(p+q-1)(-1)
=q+p-1-p-q+1
=0
Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.
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