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If a ,\ b ,\ c are in A.P. b ,\ c ,\ d a...

If `a ,\ b ,\ c` are in A.P. `b ,\ c ,\ d` are in G.P. and `1/c ,1/d ,1/e` are in A.P. prove that `a ,\ c ,\ e` are in G.P.?

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Given, `a ,\ b ,\ c` are in A.P

`2b=a+c`

`b=(a+c)/2`


`b ,\ c ,\ d` are in G.P.


`c^2=bd`

`d=c^2/b`


...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

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  2. If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,...

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  3. If a ,\ b ,\ c are in A.P. b ,\ c ,\ d are in G.P. and 1/c ,1/d ,1/e a...

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  4. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

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  6. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

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  7. If A.M. and G.M. between two numbers is in the ratio m : n then prove ...

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  8. a,b,c are positive real numbers forming a G.P. If ax^2+2bx+c=0and x^2...

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  9. If a, b,c and d are distinct positive no in AP. then

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  10. Insert 6 geometric means between 27 and 1/(81)

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  11. Insert 5 geometric means between 16 and 1/4

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  12. Insert 5 geometric means between (32)/9 and (81)/2

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  13. Find the geometric means of the following pairs of number: 2 and 8.

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  14. Find the geometric means of the following pairs of number: a^3b and a ...

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  15. Find the geometric means of the following pairs of number: -8 and -2.

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  16. If a is the G.M. of 2 and 1/4, find a

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  17. Find the two numbers whose A.M. is 25 and GM is 20.

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  18. If A and G are respectively arithmetic and geometric mean between posi...

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  19. The sum of two numbers is 6 times their geometric mean, show that numb...

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  20. If A.M. and GM. of roots of a quadratic equation are 8 and 5, respecti...

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