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If a, b, c are in A.P., prove that : a...

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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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If a(1)=1, a(2)=5 find the common difference and 5th term of A.P

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  2. If the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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

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  5. If the mth, nth and pth terms of a G.P. form three consecutive terms o...

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  6. If x,y,z are in G.P. and a^x= b^y=c^z, prove that logb a. logb c=1.

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  7. We are given two G.P.'s, one with the first term 'a' and common ratio ...

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  8. If Sn represents the sum of n terms of a G.P. whose first term and com...

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  9. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

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  10. Find the derivative of the following y=x+1/x+sinx

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  11. The sum of the first three consecutive terms of G.P. is 13 and the sum...

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

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  13. 150 workers were engaged to finish a job in a certain number of days. ...

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  14. The height of a plant at a certain date is 1.6 metre. If it increases ...

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  15. If |x|<1 and |y|<1, find the sum to infinity of the series : (x+y)+(x^...

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  16. A manufacturer reckons that the value of a machine, which costs him Rs...

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  17. Prove the following by using the principle of mathematical induction f...

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  18. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

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  19. Find the sum of n terms\ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+do...

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  20. Obtain the sum of the series : 1/1.4+1/4.7+1/7.10 + .......... to n t...

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