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If the `p^(t h)` ,`q^(t h)` and `r^(t h)` terms of a GP are a, b and c, respectively. Prove that `a^(q-r)""b^(r-p)""c^(p-q)=1` .

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Let `A` be the first term and `R` be the common difference of G.P.
`AR_(p-1)=a `
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. In a G.P. of positive terms if any terms is equal to the sum of next ...

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  2. The (m+n)t ha n d(m-n)t h terms fa G.P. ae pa n dq respectively. Show ...

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  3. If the p^(t h) ,q^(t h) and r^(t h) terms of a GP are a, b and c, r...

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  4. Find all sequences which are simultaneously A.P. and G.P.

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  5. Let S be the sum, P be the product and R be the sum of the reciprocals...

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  6. If the A.M. of two positive numbers aa n db(a > b) is twice their geom...

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  7. If one A.M., A and tow geometric means G1a n dG2 inserted between any ...

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  8. If a ,b ,c are in G.P. and a^(1//x)=b^(1//y)=c^(1//z), then x y z are ...

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  9. If A be one A.M. and p ,q be two G.M. ' s between two numbers, then...

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  10. If p ,q be two A.M. ' s and G be one G.M. between two numbers, then...

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  11. If x is positive, the sum to infinity of the series 1/(1+x)-(1-x)/((...

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  12. If (4^3)(4^6)(4^9)(4^(12))(4^(3x))=(0. 0625)^(-54) , the value of x ...

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  13. The sequence 4,12,36,108, is a G.P., because (12)/4=(36)/(12)=(108)/(3...

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  14. The sequence 1/3,-1/2,3/4,-9/8 is a G.P. with first term 1/3 and commo...

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  15. Show that the sequence given by an= 3\ (2^n),\ for all n in N , is a...

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  16. Find the 9^(th) term and the general term of the progressions: 1/4, -1...

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  17. Find the 5th term of the progression 1,((sqrt(2)-1))/(2sqrt(3)),\ ((3-...

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  18. Which term of the G.P. 5,10 ,20 ,40 , i s 5120 ?

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  19. The first term of a G.P. is 1. The sum of the third and fifth terms is...

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  20. If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, fi...

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