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If the continued product of three number...

If the continued product of three numbers in G.P. is 216 and the sum of their products in pairs is 156, find the numbers.

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To solve the problem step-by-step, we need to find three numbers in a geometric progression (G.P.) given two conditions: their continued product is 216, and the sum of their products in pairs is 156. ### Step 1: Define the Numbers in G.P. Let the three numbers in G.P. be: - \( a/r \) - \( a \) - \( ar \) ...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. Find three numbers in G.P. whose sum is 52 and the sum of whose pro...

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  2. Three numbers are in G.P. whose sum is 70. If the extremes be each ...

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  3. If the continued product of three numbers in G.P. is 216 and the sum o...

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  4. Find four numbers in G.P. whose sum is 85 and product is 4096.

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  5. Find three numbers in G.P. whose sum is 13 and the sum of whose square...

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  6. Find 4t h term from the end of the G.P. 3,6,12 ,24 , ,3072.

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  7. Which term of the G.P. 2,1/2,1/4, i s1/(128)?

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

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  9. The fourth, seventh and the last term of a G.P. are 10 ,80a n d2560 re...

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  10. If a ,b ,c are respectively the p^(t h),q^(t h)a n dr^(t h) terms of a...

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  11. In a G.P. of positive terms if any terms is equal to the sum of next ...

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  12. 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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  13. 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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  14. Find all sequences which are simultaneously A.P. and G.P.

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

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

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

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

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

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