The p^th of AP is Q,Q^th term is P. Then find (p+q)^th
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let a & d are the first term & common differnece respectively then
pth term = a+(p-1)d = q ...............1
qth term = a+(q-1)d = p ...............2
1-2
q-p = (p-q)d
d=-1
now
(p+q)th term = a + (p+q-1)d
putting value of a from eq 1
(p+q)th term = q - (p-1)d + (p+q-1)d (d =-1)
=0
pth term = a+(p-1)d = q ...............1
qth term = a+(q-1)d = p ...............2
1-2
q-p = (p-q)d
d=-1
now
(p+q)th term = a + (p+q-1)d
putting value of a from eq 1
(p+q)th term = q - (p-1)d + (p+q-1)d (d =-1)
=0
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