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If a(1),a(2),a(3), . . .,a(n) are non-ze...

If `a_(1),a_(2),a_(3), . . .,a_(n)` are non-zero real numbers such that
`(a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n)` are in

A

A.P.

B

G.P.

C

H.P.

D

none of these

Text Solution

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The correct Answer is:
B
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 2 (MULTIPLE CHOICE QUESTIONS)
  1. If (a^2+b^2+c^2) (b^2+c^2+d^2) <= (ab + bc +cd)^2 where a,b,c,d are no...

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  2. If a^(2) + 9b^(2) + 25c^(2) = abc ((15)/(a) + (5)/(b) + (3)/(c)), then...

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  3. If a(1),a(2),a(3), . . .,a(n) are non-zero real numbers such that (a...

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  4. alpha ,beta be the roots of the equation x^2 – 3x + a =0 and gamma , d...

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  5. If x, y, z be respectively the pthh, and rth terms of a G.P., then (q ...

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  6. If p, q, r are in A.P. and x, y, z in G.P., then x^(q-r) y^(r-p) z^(p ...

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  7. The sum of first three terms of a G.P. is to the sum of the first six ...

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

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  9. A.G.P. consists of 2n terms. If the sum of the terms occupying the odd...

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  10. In a sequence of (4n + 1) terms the first (2n + 1) terms are in AP wh...

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  11. If the sum of n terms of a G.P. is 3(3^(n+1))/(4^(2n)) , then find the...

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  12. Three numbers form an increasing G.P. If the middle number is doubled,...

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

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  14. If a, b and c be three distinct real number in G.P. and a + b + c = xb...

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  15. If a, b, c be in G.P., then the expression a^(2)b^(2)c^(2) ((1)/(a^(3)...

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  16. How many terms of the series 1, 4, 16,… must be taken to have their su...

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  17. The sum of n terms of the series 1 + (1)/(2) + (1)/(2^(2)) +… is less ...

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  18. The minimum value of n such that 1 + 3 + 3^(2) +...+ 3^(n) gt 1000 is

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  19. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  20. Let S1 , S2 , …. Be squares such that for each n ge 1 the length of a...

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