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If a,b,c are in A.P., then show that (i)...

If a,b,c are in A.P., then show that (i) `a^2(b+c), b^2(c+a), c^2(a+b)` are also in A.P.

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`a,b,c` are in AP.
hence,`(b−a)=(c−b)`⟶(1)
Since, `b^2(c+a)-a^2(b+c)`
`=(b−a)(ab+bc+ca)` ...
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  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., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) ...

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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 A....

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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 are i...

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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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