If p times pth term is equal to q times qth term of an ap .prove that (p+q) is equal to zero
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p(a+ (p-1)d)= q(a+(q-1)d)
ap+ p^2d - pd= aq+q^2d- qd
ap-aq+p^2d-q^2d-pd+qd=0
a(p-q)+d(p^2-q^2) -d(p-q)=0
{a(p-q)+d(p+q)(p-q)-d(p-q)=o}÷ (p-q)
a + pd+qd-d=0
a+(p+q-1)d=0
a(p+q)=0
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ap+ p^2d - pd= aq+q^2d- qd
ap-aq+p^2d-q^2d-pd+qd=0
a(p-q)+d(p^2-q^2) -d(p-q)=0
{a(p-q)+d(p+q)(p-q)-d(p-q)=o}÷ (p-q)
a + pd+qd-d=0
a+(p+q-1)d=0
a(p+q)=0
I hope it is useful...
Mark me as best answer if it is useful.
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