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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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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. 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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  2. If nine arithmetic means and nine harmonic means are inserted between ...

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

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

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

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  8. If a is the A.M. of b and c and the two geometric mean are G1 and G2...

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  9. If a,b,c ,d are distinct integer in AP such that d=a^2+b^2+c^2, then a...

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  10. The 8th and 14th term of a H.P. are 1/2 and 1/3, respectively. Find it...

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  11. Find the number of common terms to the two sequences 17,21,25,...,417 ...

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  12. If the 20th term of a H.P. is 1 and the 30th  term is -1/17, then find...

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  13. Find the sum 3/2-5/6+7/(18)-9/(54)+...oodot

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  14. If a ,b ,ca n dd are in H.P., then prove that (b+c+d)//a ,(c+d+a)//b ,...

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  15. The harmonic mean between two numbers is 21/5, their A.M. ' A ' and G....

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  16. The mth term of a H.P is n and the nth term is m . Proves that its rth...

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  17. The pth term of an A.P. is a and qth term is bdot Then find the sum o...

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  18. If agt1,bgt1andcgt1 are in G.P., then show that 1/(1+log(e)a),1/(1+log...

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  19. Solve the equation (x+1)+(x+4)+(x+7)+....+(x+28)=155.

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  20. If a ,b ,a n dc be in G.P. and a+x ,b+x ,and c+x in H.P. then find the...

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