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Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from `(n+1)^(t h)` to `(2n)^(t h)` term is `1/(r^n)` . 9873740001

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Sum of first n terms, `S_n= (a(1−r^n ))/(1−r)`
Sum of terms from `(n+1)th` to `2n th` term is, ...
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NCERT ENGLISH-SEQUENCES AND SERIES-EXERCISE 9.3
  1. The sum of two numbers is 6 times their geometric means, show that nu...

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  2. If the p^(t h),q^(t h)and r^(t h)terms of a GP are a, b and c, respec...

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  3. Show that the ratio of the sum of first n terms of a G.P. to the su...

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

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

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

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

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

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

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

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

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  13. Find the sum of the products of the corresponding terms of the sequ...

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  14. 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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  15. 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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  16. Find the 12^(t h)term of a G.P. whose 8th term is 192 and the common ...

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

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

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

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

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