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If a, b, c, d and p are different real n...

If `a, b, c, d` and `p` are different real numbers such that `(a^2+b^2+c^2).p^2-2(ab+b c+cd) p +(b^2+c^2+d^2) le 0`, then show that `a, b, c` and `d` are in `G.P`.

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V PUBLICATION-SEQUENCES AND SERIES-QUESTIONBANK
  1. If p^(th), q^ (th) , r^ (th) and s^ (th) terms of an A.P are in G.P, t...

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  2. If a, b, c are in AP and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, z ar...

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  3. If a, b, c, d and p are different real numbers such that (a^2+b^2+c^2)...

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  4. If p,q ,r are in G . P, and the equations, p x^2+2 q x+r=0 and d x^2+2...

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  5. Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A . P is eq...

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  6. If the sum of three numbers in an. A.P. is 24 and their product is 440...

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  7. If S1,S2 and S3 are respectively the sums of n, 2n and 3n terms of an ...

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  8. Find the sum of multiple of 7 between 200 and 400.

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  9. Find the sum of integers from 1 to 100 that are divisible-by 2 or 5 .

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  10. Find the sum of all two digit numbers which when divided by 4, yields ...

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  11. If f is a function satisfying f(x+y)=f(x) . f(y) 'for all x, y in N su...

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  12. The sum of some terms of G.P.is 315 . whose first term and the common ...

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  13. The first term of a G.P is 1. The sum of the third and fifth terms is ...

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  14. The sum of three numbers in G.P is 56 : If we subtract 1,7,21 from the...

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  15. A G.P consists of an even number of terms. If the sum of all the term...

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  16. The sum of the first four terms of an A.Pis 56. The sum of the last fo...

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  17. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+d x)/(c-d x)(x ne 0), then show ...

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  18. Let S be the sum, P, the product and R the sum of reciprocals of n ter...

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  19. The p^ (th) , q^ (th) and r^ (th) terms of an A.P. are a, b, c respe...

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  20. If a (1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P. Prove that a, b, c ...

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