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If the sum of three numbers in G.P. is 3...

If the sum of three numbers in G.P. is 38 and their product is 1728, find them.

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To solve the problem, we need to find three numbers in Geometric Progression (G.P.) given that their sum is 38 and their product is 1728. Let's denote the three numbers as \( \frac{a}{r}, a, ar \), where \( a \) is the middle term and \( r \) is the common ratio. ### Step-by-step Solution: 1. **Set Up the Equations**: - The sum of the three numbers can be expressed as: \[ \frac{a}{r} + a + ar = 38 ...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. If x^a=x^(b//2)z^(b//2)=z^c , then prove that 1/a ,1/b ,1/c are in A.P...

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  2. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , t...

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  3. If the sum of three numbers in G.P. is 38 and their product is 1728, ...

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  4. If the p^(t h) and q^(t h) terms of a G.P. are q and p respectively, s...

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  5. In a finite G.P. the product of the terms equidistant from the begi...

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  6. The product of first three terms of a G.P. is 1000. If 6 added to its ...

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  7. Find three numbers in G.P. whose sum is 52 and the sum of whose pro...

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

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

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

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

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

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

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

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

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

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  18. 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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  19. 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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  20. Find all sequences which are simultaneously A.P. and G.P.

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