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If the 4th and 9th terms of a G.P. be 54...

If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P.

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Let a be the first term and r be the common ratio of the given GP.
Then,
`T_4=54⇒ar^(4−1)=54⇒ar^3=54 . . .. (i)`
And,
`T_9=13122⇒ar^(9−1)=13122``=>ar^8=13122 . . .(ii)`
On dividing (ii) by (i), we get
...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. Which term of the G.P. 5,10 ,20 ,40 , i s 5120 ?

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  2. The first term of a G.P. is 1. The sum of the third and fifth terms is...

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  3. If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, fi...

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  4. Find a G.P. for which sum of the first two terms is -4 and the fifth...

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  5. (ii)If the third term of G.P.is 4, then find the product of first five...

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  6. If the p t h ,\ q t h\ a n d\ r t h terms of a G.P. are a ,\ b ,\ c re...

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  9. What will Rs. 500 amounts to in 10 years after its deposit in a bank w...

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  10. A manufacturer reckons that the value of a machine, which costs him Rs...

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  11. If the first and the nth terms of a G.P., are aa n db , respectively, ...

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  12. Show that the products of the corresponding terms o the sequences a ,\...

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  13. If p^(t h),\ q^(t h),\ r^(t h)a n d\ s^(t h) terms of an A.P. are in G...

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  14. Show that each of one of the following progression is a G.P. Also, fin...

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  15. Show that each of one of the following progression is a G.P. Also, fin...

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  16. Show that each of one of the following progression is a G.P. Also, ...

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  17. Show that each of one of the following progression is a G.P. Also, ...

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  18. Show that the sequence defined by an=2/(3^n),\ n in N\ is a G.P.

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  19. Find: the ninth term of the G.P. 1,4,16,64,………

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  20. Find: the 10th term of the G.P. -3/4,1/2,-1/3,2/9, dot

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