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If the 4th, 10th and 16th terms of a G.P...

If the `4th`, `10th` and `16th` terms of a G.P. are `x, y`, and `z` respectively. Prove that `x, y, z` are in G.P.

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Given, `a=` first term, `r=` common ratio

General term `= ar^(n-1)`

`x=ar^3`

`y=ar^9`

`z=ar^15`

To prove: `y^2=xz`

`RHS= xz`

`=ar^3*ar^15`

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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. If a, b, c are in G. P., prove that a^2+ b^2, ab + bc, b^2 +c^2 are al...

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  2. If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c...

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  3. If the 4th, 10th and 16th terms of a G.P. are x, y, and z respectivel...

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

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  6. 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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  7. 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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  8. If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are bo...

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

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

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

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

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

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

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

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

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

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

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

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

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