If a, b, c are positive and are the pth, qth, and rth terms, respectively, of a G.P., then Δ=logap1logbq1logcr1 is
0
log (abc)
-(p + q + r)
none of these
Let the first term of G.P. be A and common ratio be R. Then,
a=ARp−1
⇒ loga=logA+(p−1)logR, etc. ⇒logap1logbq1logcr1=logA+(p−1)logRp1logA+(q−1)logRq1logA+(r−1)logRr1
=(p−1)logRp1(q−1)logRq1(r−1)logRr1 C1→C1−(logA)C3=logR(p−1)p1(q−1)q1(r−1)r1=logRpp1qq1rr1=0 C1→C1+C3