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If x ,1,a n dz are in A.P. and x ,2,a n ...

If `x ,1,a n dz` are in A.P. and `x ,2,a n dz` are in G.P., then prove that `x ,a n d4,z` are in H.P.

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. a, b, x are in AP, a, b, y are in GP and a, b, z are in HP, then prove...

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  2. If a , b , c , are in A P ,a^2,b^2,c^2 are in HP, then prove that eith...

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  3. 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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  4. If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...

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  5. The values of xyz is 15/2 or 18/5 according as the series a, x, y, z, ...

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  6. In a A.P & an H.P have the same first term, the same last term & the s...

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  7. l, m, n are three numbers in G.P., a is the first term of an A.P., who...

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  8. Three unequal numbers are in HP and their squares are in AP. Show that...

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  9. Insert 12 arithmetic means between -3.5 and -42.5.

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  10. Insert 6 geometric means between 27 and 1/(81)dot

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  11. Find the 5th harmonic mean when n harmonic means are inserted between ...

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  12. If n A.Ms are inserted between two numbers, prove that the sum of the ...

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  13. Prove that the product n geometric means between two quantities is equ...

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  14. If n arithmetic means xare inserted between 1 and 31 such that the 7^(...

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  15. The sum of two numbers is (13)/6dot An even number of arithmetic means...

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  16. If a, b, c, d are positive numbers in HP then prove that ad gt bc.

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  17. If a, b, c are in AP or GP ot HP where a>0, b>0, c>0 then prove that b...

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  18. If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9

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  19. If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2.

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  20. If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)...

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