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If a ,b ,c are respectively the p^(t h),...

If `a ,b ,c` are respectively the `p^(t h),q^(t h)a n dr^(t h)` terms of a G.P. show that `(q-r)loga+(r-p)logb+(p-q)logc=0.`

A

1

B

0

C

-1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let A be first term and R be the common ratio of the G.P. Then,
`a=AR^(p-1)rArrloga=logA+(p-1)logR` . . . (i)
`b=AR^(q-1)rArrlogb=logA+(q-1)logR` . . .(ii)
`c=AR^(r-1)rArrlogc=logA+(r-1)logR` . . .(iii)
Multiplying (i), (ii) and (iii) by (q-r),(r-p) and (p-q) respectively and adding, we get
`(q-r)loga+(r-p)logb+(p-q)logc=0rArrDelta=0`
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  12. If Sn denotes the sum of n terms of an A.P. whose common difference is...

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  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

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  15. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

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  16. If three numbers are in G.P., then the numbers obtained by adding the ...

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  21. The first three of four given numbers are in G.P. and their last three...

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