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If a^2(b+c),b^2(c+a),c^2(a+b), are in A....

If `a^2(b+c),b^2(c+a),c^2(a+b),` are in A.P. show that either `a ,b ,c` are in A.P., or `a b+b c+c a=0.`

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MODERN PUBLICATION-SEQUENCES AND SERIES-REVESION EXERCISE
  1. if the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  2. If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

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  3. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

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  4. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

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  5. If x,y,z are in G.P and a^x=b^y=c^z,then

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  6. We are given two G.P's one with the first term a and common ratio r an...

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  7. if sn, denotes the sum of n terms of a GP whose first term and common ...

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  8. If p, q, r are in G.P. and the equations, p x^2+2q x+r=0and dx^2+2e x...

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  9. If S(n) denotes the sum of n terms of a G.P., prove that: (S(10)-S(20)...

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  10. The sum of the first thre consecutive terms of G.P is 13 and the sum o...

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  11. If 1/(a+b)+1/(b+c)=1/b, prove that a,b,c are in G.P.

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  12. 150 workers were engaged to finish a job in a certain number of days. ...

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  13. If |x|<1a n d|y|<1, find the sum of infinity of the following series: ...

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  14. A manufacture reckons that the value of a machine which costs him Rs. ...

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  15. The sum of the series : 1+1/(1+2)+1/(1+2+3)+...... upto 10 terms is :

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  16. Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

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  17. Obtain the sum of the series 1/4+1/16+1/64……………….to oo

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  18. Show that (1xx2^2+2xx3^2+dotdotdot+nxx(n+1)^2)/(1^2xx2+2^2xx3+dotdotdo...

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  19. What will Rs. 500 amounts to in 10 years after its deposit in a bank w...

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  20. A man deposited Rs 10000 in a bank at the rate of 5% simple interes...

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