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If the A.M. between two numbers exceeds ...

If the A.M. between two numbers exceeds their G.M. by 2 and the GM. Exceeds their H.M. by 8/5, find the numbers.

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

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Find the sum of the series 1-3x+5x^2-7x^3+ ton terms.

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  2. In a geometric progression consisting of positive terms, each term ...

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  3. If the A.M. between two numbers exceeds their G.M. by 2 and the GM. ...

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  4. The AM of two given positive numbers is 2. If the larger number is inc...

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  5. Find the sum of the series 1+3x+5x^2+7x^3+..........upto n terms.

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  6. If (a-x)/(p x)=(a-y)/(q y)=(a-z)/(rz) and p ,q ,and r are in A.P., the...

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  7. Find the sum of n terms of the series 1+4/5+7/(5^2)+10/5^3+......

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  8. Find the sum (1^2)/2-(3^2)/(2^2)+(5^2)/(2^3)-(7^2)/(2^4)+....oodot

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  9. If H is the harmonic mean between P and Q then find the value of H//P+...

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  10. If Tr=r(r^2-1), then find sum(r=2)^oo1/Trdot

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  11. Insert four H.M.’s between 2/3 and 2/13.

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  12. If a , b ,a n dc are respectively, the pth, qth , and rth terms of a G...

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  13. The A.M. and H.M. between two numbers are 27 and 12, respectively, t...

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  14. If a ,a1, a2, a3, a(2n),b are in A.P. and a ,g1,g2,g3, ,g(2n),b . are...

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  15. If nine arithmetic means and nine harmonic means are inserted between ...

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  16. If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove tha...

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  17. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

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  18. If a,b,c ,d and p are distinct real number such that (a^2+b^2+c^2)p^2-...

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  19. If A.M. and G.M. between two numbers is in the ratio m : n then prove...

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  20. Prove that (666....6)^2+(888....8)=4444.....4.

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