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If A and G be A.M. and G.M., respectivel...

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

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. 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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  2. Find n such that (a^n+b^n)/(a^(n-1)+b^(n-1)) may be the geometric mean...

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  3. If A and G be A.M. and G.M., respectively between two positive numbers...

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  4. If A and G are the A.M. and G.M. respectively between any two distinct...

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  5. The sum of first three terms of a G.P. is 39/10 and their product is 1...

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  6. The sum of first three terms of a GP. is 13/12 and their product is - ...

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

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  8. The sum of three numbers which are consecutive terms of an A.P. is 21....

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  9. There are four numbers such that the first three of them form an arith...

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  10. The sum of first three terms of a G.P. is 7 and the sum of their squar...

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  11. Find three numbers in G.P. : whose sum is 30 and whose Product is 216.

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  12. Find three numbers in G.P. : whose sum is 38 and whose product is 1728...

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  13. Find three numbers in G.P. whose sum is 35 and sum of their squares is...

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  14. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  15. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  16. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  17. If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G....

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  18. If a,b,c, d are in G.P., show that : a^(2)+b^(2), b^(2)+ c^(2) and c...

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  19. If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (...

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

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