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If the A.M. between pth and qth terms of...

If the A.M. between pth and qth terms of an A.P. be equal to the A.M. between rth and sth terms of the A.P., show that p +q= r+s.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P., then show that : b=(2ac)/(...

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  2. If a(1)=1, a(2)=5 find the common difference and 5th term of A.P

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

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  4. 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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  5. 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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  6. If the mth, nth and pth terms of a G.P. form three consecutive terms o...

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

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

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

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

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

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

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  14. 150 workers were engaged to finish a job in a certain number of days. ...

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

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

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

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

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

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