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If mth, nth and pth terms of a G.P. form...

If mth, nth and pth terms of a G.P. form three consecutive terms of a G.P. Prove that `m ,n ,and p` form three consecutive terms of an arithmetic system.

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Let `a` be the first term and` r` be the common ratio of the given GP.
Then, `T_m = a r^( m − 1 )`
` T_n = a r^( n − 1 )`
` T_m=ar^(m-1)`,
...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. The sum of three numbers a ,b ,c in A.P. is 18 . If a and b are each i...

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  2. If a ,b ,c are in G.P., prove that: 1) a(b^2+c^2)=c(a^2+b^2) , 2)...

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  3. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

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  4. If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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