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If (p^2+q^2), (pq+qr), (q^2+r^2) are in ...

If `(p^2+q^2), (pq+qr), (q^2+r^2)` are in GP then Prove that `p, q, r` are in G.P.

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If a,b, c are in GP, Prove that a^2, b^2 , c^2 are in GP.

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  2. If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P....

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  3. If (p^2+q^2), (pq+qr), (q^2+r^2) are in GP then Prove that p, q, r are...

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  4. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

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  5. Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5...

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  6. Let the sum of first three terms of G.P. with real terms be 13/12 and ...

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  7. Given a,b,c are in A.P.,b,c,d are in G.P and c,d,e are in H.P .If a=2 ...

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  8. The terms a1,a2,a3 form an arithmetic sequence whose sum is 18.The ter...

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  9. Let f(x)=2x+1. Then the number of real number of real values of x for ...

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  10. Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The inte...

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  11. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4 and t2+...

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  12. If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G....

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  13. If a,b,c,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2)...

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  14. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

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  15. If a, b, care in GP then prove that a^3, b^3, c^3 are in GP.

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  16. The second term of an H.P. is 3/14 and the fifth term is 1/10 . Find...

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  17. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

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  18. If the sixth term of an H.P. is 10 and the 11th term is 18 Find the 16...

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  19. If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then ...

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  20. Let Tr be the rth term of an A.P., for r=1,2,3,..... If for some pos...

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