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If one geometric mean G and two arithmet...

If one geometric mean G and two arithmetic means p, q be inserted between two given numbers, then prove that,
`G^(2) = (2p - q) (2q - p)`.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Long Answer Type Questions)
  1. Find the sum to n terms of each of the following series : 1 + 11 + 1...

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

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  3. 0.8 + 0.88 + 0.888 + …

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

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

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

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

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

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

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

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

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

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

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  15. A, B, C have together Rs. 5700 and the amount of money possessed by th...

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  16. If the (m + 1)th, (n + 1)th and (r + 1)th terms of an A.P. are in G.P....

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  17. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

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  18. The pth , qth and rth terms of an A.P. are in G.P. Prove that the comm...

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  19. If a(1), a(2),…,a(n) are in G.P., then show that (1)/(a(1)^(2) - a(2...

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  20. If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) ...

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