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Which term of the following sequences:(a) `2,2sqrt(2),4,. . . is 128?` (b) `sqrt(3),3,3sqrt(3),. . . is 729?`(c) `1/3,1/9,1/(27),`. . . is `1/(19683)?`

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(a) The given sequence is, `2,2sqrt2,4........`
clearly given sequence is in GP
with `a=2` and `r=(2sqrt2)/2=sqrt2`
Let the `n^(th)` term of the given sequence be `128`
...
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NCERT-SEQUENCES AND SERIES-EXERCISE 9.3
  1. Show that the ratio of the sum of first n terms of a G.P. to the sum ...

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

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  3. If the 4^(t h), 10^(t h)and 16^(t h)terms of a G.P. are x, y and z, r...

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  4. The sum of first three terms of a G.P. is 16 and the sum of the next ...

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  5. Given a G.P. with a = 729 and 7^(t h)term 64, determine S7.

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  6. The sum of first three terms of a G.P. is (39)/(10) and their product ...

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  7. How many terms of G.P. 3,3^2,3^3,dotdotdotare needed to give the sum 1...

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  8. Find the sum to indicated number of terms in each of the geometric pr...

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  9. Evaluate sum(k=1)^(11)(2+3^k)

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  10. Find the sum to n terms of the sequence, 8, 88, 888, 8888 . . . .

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  11. Find the sum of the products of the corresponding terms of the sequen...

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  12. Find the 20^(t h)and n^(t h)terms of the G.P. 5/2,5/4,5/8,dotdotdot

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  13. The 5^(t h), 8^(t h)and 11^(t h)terms of a G.P. are p, q and s, respe...

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  14. Find the 12^(t h)term of a G.P. whose 8th term is 192 and the common ...

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  15. Which term of the following sequences:(a) 2,2sqrt(2),4,. . . is 128? (...

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  16. The 4^(t h)term of a G.P. is square of its second term, and the first...

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  17. Find the sum to indicated number of terms in each of the geometric pr...

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  18. For what value of x, the number -2/7,x ,-2/7are in G.P.?

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  19. Find the sum to indicated number of terms in each of the geometric pr...

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  20. Find the sum to indicated number of terms in each of the geometric pr...

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