Question

in ap if p,q,r term is c,b,a respectively and in gp if p,q, r be term is a,b,c respectively get the value of a^b-c.b^c-a.c^a-b​

Answer 1

Answer:

Question



If the pth,qth and rth terms of a G.P. are a, b and c respectively. Prove that aq−rbr−pcp−q=1.

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Solution



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Let A be the first term and R be the common ratio. Then, 

a=pth term =AR(p−1)

b=qth term =AR(q−1)

c=rth term =AR(r−1)

Substituting values of a,b & c, we get,

a(q−r).b(r−p).c(p−q)

=[AR(p−1)](q−r).[AR(q−1)](r−p).[AR(r−1)](p−q)

=A(q−r)R(p−1)(q−r).A(r−p)R(q−1)(r−p).A(p−q)R(r−1)(p−q)

=A0R0=1