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If one A.M., A and two geometric means G...

If one A.M., `A` and two geometric means `G_1a n dG_2` inserted between any two positive numbers, show that `(G1 ^2)/(G2)+(G2 ^2)/(G_1)=2Adot`

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. If the A.M. of two positive numbers aa n db(a > b) is twice their geom...

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  2. Find the sum of the following geometric progression: 4,8,16,32....to 8...

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  3. If one A.M., A and two geometric means G1a n dG2 inserted between any ...

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

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

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

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

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

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

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

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

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  14. Which term of the G.P. 5,10 ,20 ,40 ,..... i s5120 ?

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

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

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  17. Find a G.P. for which sum of the first two terms is - 4 and the fift...

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  18. If the third term of G.P.is 4, then find the product of first five ter...

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  19. If the p t h ,\ q t h\ a n d\ r t h terms of a G.P. are a ,\ b ,\ c re...

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  20. Find four numbers forming a geometric progression in which the third ...

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