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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., then show that `p+q=r+s`

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If the A.M. between p^(th) and q^(th) terms of an A.P. , be equal to the A.M., between m^(th) and n^(th) terms of the A.P. , then show that p + q = m + n .

If the A.M. between mth and nth terms of an A.P. be equal to the A.M. between pth and qth terms of an A.P. then prove that m+n=p+q .

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MODERN PUBLICATION-SEQUENCES AND SERIES-REVESION EXERCISE
  1. "If " a^(2), b^(2), c^(2)" are in A.P., prove that "(1)/(b+c),(1)/(c+a...

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  2. If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P. then show that b=(2ac)/(a+c...

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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 ,c ar...

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

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

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

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

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

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

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

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

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

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

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

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

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