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If the arithmetic mean of y and z be x a...

If the arithmetic mean of y and z be x and that of `(1)/(x)` and `(1)/(y)` be `(1)/(z)`, then show that x, y, z are in G.P.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Long Answer Type Questions)
  1. If A and G be the A.M. and G.M. of two numbers , show that the numbers...

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  2. If a, b, c form an A.P. and b, c, a form a G.P., show that (1)/(c ), (...

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  3. If the arithmetic mean of y and z be x and that of (1)/(x) and (1)/(y)...

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  4. The sum of three numbers in A.P. is 15. If 1, 4 and 19 are added to th...

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  5. The sum of three numbers in A.P. is 18. If 2, 2, 6 are added respectiv...

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  6. Three terms are in G.P. Their product is 216. If 4 be added to the fir...

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  7. Find the sum to n terms of each of the following series : 1 + 11 + 1...

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  8. Find the sum to n terms of each of the following series : 2 + 22 + ...

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  9. 0.8 + 0.88 + 0.888 + …

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  10. Find the sum to n terms of each of the following series : 0.6 + 0.6...

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  11. Find the sum to n terms of each of the following series : 1 + 4 + 1...

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  12. Three unequal numbers a, b, c are in A.P. and a, (b-a), (c-a) are in G...

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  13. If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (...

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  14. The first term of an A.P. is the same as that of a G.P., the common di...

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  15. Find the sum to n terms : (1)/(2) + (3)/(2^(2)) + (5)/(2^(3)) +…+ (2...

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  16. Find the sum to n terms : 2 + 3.3 + 4.3^(2) + 5.3^(3) +…

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  17. Find the sum to n terms : 12 + 105 + 1008 + 10011+…

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  18. Find the sum to n terms : 12 + 14 + 24 + 58 + 164+…

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  19. The rth term of a series is (2r + 1)2^(r ), find the sum of first n te...

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  20. If one geometric mean G and two arithmetic means p, q be inserted betw...

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