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If x, y, z are three positive numbers fo...

If x, y, z are three positive numbers forming a geometric sequence, then show that `log_a x, log_a y,log_a z` form an arithmetic sequence , a being positive and not equal to 1.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. The terms of a G.P. with first term ‘a’ and common ratio ‘r’ are squar...

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  2. If the first and the nth terms of a GP are a and b respectively and if...

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  3. If x, y, z are three positive numbers forming a geometric sequence, th...

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  4. The (m+n)th and (m-n)th terms of a GP are p and q, respectively. Then,...

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  5. If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c...

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

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  7. Evaluate : sum(i=1)^18 (2^i +3^(i-1)).

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  8. Find the sum to indicated number of terms of the geometric progression...

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  9. Find the sums of the indicated number of terms of the following geomet...

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  10. Find the sums of the indicated number of terms of the following geomet...

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  11. Find the sum to indicated number of terms of the geometric progression...

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  12. Find the sum to indicated number of terms of the geometric progression...

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  13. Find the sum to indicated number of terms of the geometric progression...

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  14. Find the sums of the indicated number of terms of the following geomet...

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  15. How many terms of G.P. 3, 3^2, 3^3, ... are needed to give the sum 120...

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  16. How many terms of a G.P. 3,3/2,3/4,......... are needed to give the su...

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  17. Determine the number n of terms of the G.P. 3,6,12, .......... so that...

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  18. Given a G.P. with a= 1,r= sqrt2. Find S20.

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  19. Given a G.P. with a= 729 and 7th term 64, determine S7.

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  20. If {an} is a G.P. and a1=4,r=5, find a6 and S6.

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