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If a, b, c are in A.P., prove that a^(2)...

If a, b, c are in A.P., prove that `a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)" are also in A.P."`

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If a, b, c are in A.P., prove that: (i) 1/(bc) , 1/(ca), 1/(ab) are in A.P. (ii) (b+c)^2- a^2 ,(a+c)^2- b^2 , (b+a)^2- c^2 are in A.P.

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. If 2/3, k ,5/8 are in A.P., find the value of kdot

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  2. If 1/a ,1/b ,1/c are in A.P. prove that: (b+c)/a ,(c+a)/b ,(a+b)/c are...

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  3. If a, b, c are in A.P., prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)" a...

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  4. If a, b, c are in A.P, then show that: b+c-a ,\ c+a-b ,\ a+b-c are in ...

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  5. If a, b, c are in A.P, then show that: \ b c-a^2,\ c a-b^2,\ a b-c^2 a...

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  6. If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are als...

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  7. If (b+c)/a ,(c+a)/b ,(a+b)/c are in A.P., prove that : b c ,\ c a ,\ a...

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  8. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

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  9. Insert 3 arithmetic means between 3 and 19.

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  10. For what value of n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n) is the arithmeti...

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  11. Between 1 and 31 are inserted m arithmetic mean so that the ratio of t...

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  12. if the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  13. Find the A.M. between: 7 and 13

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  14. Find the A.M. between: 12\ a n d-8

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  15. Find the A.M. between: (x-y)a n d\ (x+y)

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  16. Insert 4 A.M.s between 4 and 19.

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  17. Insert 7 A.M.s between 2 and 17.

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  18. Insert six A.M.s between 15 and -13.

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  19. There are n A.M.s between 3 and 17. The ratio of the last mean to the ...

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  20. Insert AMs between 7 and 71 such that 5^(th) AM is 27. Also find the n...

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