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If A and G be the A.M. and G.M. of two n...

If A and G be the A.M. and G.M. of two numbers , show that the numbers are `A +- sqrt(A^(2) - G^(2))`.

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If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A pm sqrt((A+G )(A−G )) .

If A and G are the A.M.and G.M. of two unequal positive numbers a and b, show that A>G>G^2/A

If the G.M. and H.M. of two numbers are 15 and 9 respectively, find the numbers.

If the A.M. of two numbers be twice their G.M., prove that two numbers are in the ratio (2 + sqrt(3)) : (2 - sqrt(3)) .

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a:b =(m+sqrt(m^2-n^2)):(m-sqrt(m^(2)-n^2)) .

If the A.M. and H.M. of two numbers are 15 and 9(3)/(5) respectively, find the numbers.

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

If the ratio of G.M. of two numbers to their H.M. is 5 : 4 , prove that the numbers are in the ratio of 4 : 1 .

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

G.M. of 3, 6, 24, 48 is

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Long Answer Type Questions)
  1. When a certain golf-ball is dropped on a piece of pavement, it bounces...

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  2. If the A.M. of two numbers be twice their G.M., prove that two numbers...

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  3. If A and G be the A.M. and G.M. of two numbers , show that the numbers...

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

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

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

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

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

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

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

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  11. 0.8 + 0.88 + 0.888 + …

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

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

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

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

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

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

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

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

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