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If S1,S2,S3 be the sum of n, 2n, 3n term...

If `S_1,S_2,S_3` be the sum of n, 2n, 3n terms of a G.P., show that : `S_1(S_3-S_2)= (S_2-S_1)^2`.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
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  2. Find the sum of the products of the corresponding terms of the sequenc...

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  3. If S1,S2,S3 be the sum of n, 2n, 3n terms of a G.P., show that : S1(S3...

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  8. Insert 4 geometric means between 6 and 192.

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  9. The A.M. between two numbers is 20 and their G.M. is 16. Find the numb...

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  10. a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c r...

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  11. a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c r...

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  12. The sum of two numbers is 6 times their geometric mean, show that numb...

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  13. The ratio of the.A.M. and G.M. of two positive numbers a and b is m : ...

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  14. If G1 is the first of n geometric means between a and b, show that : G...

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  15. If G is the geometric mean between two distinct positive numbers a and...

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  16. If A.M. and G.M pf roots of a quadratic equation are 8 and 5 respectiv...

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  17. If one geometric mean G and two arithmetic means p amd q be inserted b...

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  18. If a is the A.M. of b and c and the two geometric means are G(1) and G...

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  19. If p ,q, r are in A.P., a is G.M. between p, q and b is G.M. between q...

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  20. Find n such that (a^n+b^n)/(a^(n-1)+b^(n-1)) may be the geometric mean...

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