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If one arithmetic mean A and two geometr...

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

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Short Answer Type Questions)
  1. Shri A. K. Roy borrows Rs. 6000 to repay the amount with interest of R...

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  2. A man borrows Rs. 19682 without interest and agrees to repay the money...

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  3. The A.M. of two numbers is 15 and their G.M. is 12. Find the numbers.

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  4. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

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  5. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

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  6. If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^...

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  7. The sum of three numbers in G.P. is 70. If each of the two extremes be...

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  8. Let t(r) be the rth term of an A.P. If t(2), t(8) and t(32) are in G.P...

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  9. If p, q, r be in arithmetic progression, then show that the pth, qth a...

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  10. The nth term of a series is 3^(n) + 2n, find the sum of first n terms ...

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  11. If one arithmetic mean A and two geometric means p, q be inserted betw...

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  12. If A is the A.M. and G is the G.M. of two unequal positive real number...

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  13. Between two positive real numbers a and b, one arithmetic mean A and t...

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  14. If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2...

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  15. If a is A.M. of two positive numbers b and c and two G.M's between b a...

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  16. If G is the G.M. between two positive numbers a and b, show that (1)/(...

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  17. If sum of the square of three different terms in G.P. is S^(2) their s...

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  18. Show that sum of n G.M.s between a and b is ((ab^((1)/(n+1))-ba^((1)/(...

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  19. Evaluate : Sigma(K=1)^(7) [((1)/(5))^(2K+1).(7)^(K-1)]

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  20. The A.M. between m and n and the G.M. between a and b are each equal t...

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