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In a G.P. it is given that T(p-1)+T(p+1)...

In a G.P. it is given that `T_(p-1)+T_(p+1)=3T_(p).` Prove that its common ratio is an irrational number.

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NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Exercise 9F
  1. Find the 8th term of the G.P. sqrt(3),(1)/(sqrt(3)),(1)/(3sqrt(3)),......

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  2. Find the number of terms in the G.P. 1, 2, 4, 8, ... 4096.

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  3. Find the number of terms in the G.P. 1, - 3, 9, ... - 2187.

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  4. Find the 5th term from the end of the G .P. (1)/(512),(1)/(256),(1)/(1...

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  5. Find the, 4th terin from the end of the G .P. (5)/(2),(15)/(8),(45)/(3...

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  6. Which term of the progression sqrt(3),3,3sqrt(3)... is 729 ?

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  7. Which term of the progression 2, 8, 32,… is 131072 ?

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  8. If the nth terms of the progression 5, 10, 20, … and progression 1280,...

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  9. The 3rd, 7th and 11th terms of a G.P. are x, y and z respectively, the...

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  10. The 3rd and 6th terms of a G.P. are 40 and 320, then find the progress...

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  11. Find the G.P. whose 2nd and 5th terms are -(3)/(2)" and "(81)/(16) r...

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  12. if a G.P (p+q)th term = m and (p-q) th term = n , then find its p th t...

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  13. Find the G.P. whose 2nd term is 12 and 6th term is 27 times the 3rd te...

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  14. The first term of a G.P. is -3. If the 4th term of this G.P. is the sq...

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  15. The 4th, 7th and last terms of a G.P. are 10,80 and 2560 respectively....

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  16. Find the 4 terms in G .P. in which 3rd term is 9 more than the first t...

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

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  18. In a G.P. it is given that T(p-1)+T(p+1)=3T(p). Prove that its common ...

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  19. If k, k + 1 and k + 3 are in G.P. then find the value of k.

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  20. The product of 3rd and 8th terms of a G.P. is 243 and its 4th term is ...

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