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Three numbers are in A.P. and their sum ...

Three numbers are in A.P. and their sum is `15`. If `1,3,9` be added to them respectively they form a G.P. Find the numbers.

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Let the numbers are in A.P. `=a-d, a, a+d`

`a-d+a+a+d=15`

`3a=15`

`a=5`

Given, if `1,3,9` be added to them respectively. `a-d+1=6-d` `a+3=8` `a+d+9=14+d` ...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. If a ,\ b ,\ c are in G.P. prove that 1/((log)a m),1/((log)b m),1/((lo...

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  2. Find k such that k+9, k-6 and 4 from three consecutive terms of a G.P.

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  3. Three numbers are in A.P. and their sum is 15. If 1,3,9 be added to th...

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  4. The sum of three numbers which are consecutive terms of an A.P. is 21....

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  5. The sum of three numbers in G.P. is 56. If we subtract 1,7,21 from the...

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  6. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

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  7. If a , b, c are in G.P., prove that the following are also in G.P.: a^...

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  8. 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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  9. 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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  10. If the 4th, 10th and 16th terms of a G.P. are x, y, and z respectivel...

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

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  13. 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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  14. 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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  15. 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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  16. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

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

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

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

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

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