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If (a(2)a(3))/(a(1)a(4))=(a(2)+a(3))/(a(...

If `(a_(2)a_(3))/(a_(1)a_(4))=(a_(2)+a_(3))/(a_(1)+a_(4))=3((a_(2)-a_(3))/(a_(1)-a_(4)))`, then `a_(1),a_(2),a_(3),a_(4)` are in

A

`A.P`

B

`G.P`

C

`H.P`

D

none of these

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The correct Answer is:
C
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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

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common rario r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

,1+a_(1),a_(2),a_(3)a_(1),1+a_(2),a_(3)a_(1),a_(2),1+a_(3)]|=0, then

if a_(1),a_(2),a+_(3)……,a_(12) are in A.P and Delta_(1)= |{:(a_(1)a_(5),,a_(1),,a_(2)),(a_(2)a_(6),,a_(2),,a_(3)),(a_(3)a_(7),,a_(3),,a_(4)):}| Delta_(3)= |{:(a_(2)b_(10),,a_(2),,a_(3)),(a_(3)a_(11),,a_(3),,a_(4)),(a_(3)a_(12),,a_(4),,a_(5)):}| then Delta_(2):Delta_(2)= "_____"

If a_(0),a_(1),a_(2),a_(3) are all the positive,then 4a_(0)x^(3)+3a_(1)x^(2)+2a_(2)x+a_(3)=0 has least one root in (-1,0) if ( a )a_(0)+a_(2)=a_(1)+a_(3) and 4a_(0)+2a_(2)>3a_(1)+a_(3)(b)4a_(0)+2a_(2)<3a_(1)+a_(3)(c)4a_(0)+2a_(2)=3a_(1)+a_(0) and 4a_(0)+a_(2)

a1,a2,a3.....an are in H.P. (a_(1))/(a_(2)+a_(3)+ . . .+a_(n)),(a_(2))/(a_(1)+a_(3)+ . . . +a_(n)),(a_(3))/(a_(1)+a_(2)+a_(4)+ . . .+a_(n)), . . .,(a_(n))/(a_(1)+a_(2)+ . . . +a_(n-1)) are in

If a_(1),a_(2),...,.,a_(10) are positive numbers in arithmetic progression such that (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))+...*+(1)/(a_(9)a_(10))=(9)/(64) and (1)/(a_(1)a_(10))+(1)/(a_(2)a_(9))+......(1)/(a_(10)a_(1))=(1)/(10)((1)/(a_(1))+...+(1)/(a_(10))) then the value of (2)/(5)((a_(1))/(a_(10))+(a_(10))/(a_(1))) is

FIITJEE-PROGRESSION & SERIES -SOLVED PROBLEMS (OBJECTIVE)
  1. Three friends whose ages form a G.P ivide a certain sum of money in in...

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  2. The sum to n terms of the series (n^(2)-1^(2))+2(n^(2)-2^(2))+3(n^(2...

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  3. If (a(2)a(3))/(a(1)a(4))=(a(2)+a(3))/(a(1)+a(4))=3((a(2)-a(3))/(a(1)-a...

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  4. If ar>0, r in N and a1.a2,....a(2n) are in A.P then (a1+a2)/(sqrta1+sq...

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  5. Find the greatest value of x^2y^3, w h e r exa n dy lie in the first q...

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  6. Let p,q,repsilonR^(+) and 27pqr>=(p+q+r)^3 and 3p+4q+5r=12 then p^3+q^...

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  7. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

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  8. If three positive unequal numbers a, b, c are in H.P., then

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  9. A geometric progression of real numbers is such that the sum of its ...

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  10. If (a+bk)/(a-bk) = (b+ck)/(b-ck) = (c-dk)/(c-dk) where k != 0 , a, b ,...

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  11. If three positive numbers a,b,c are in A.P ad tan^(-1)a,tan^(-1)b,tan^...

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  12. Find the sum n terms of seires tan theta+1/2tantheta/2+1/(2^2)tantheta...

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  13. sum (k=1)^(n) tan^(-1). 1/(1+k+k^(2)) is equal to

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  14. Find the sum of n terms the series: 1/(costheta+cos3theta0+1/(costheta...

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  15. The 100^(th) term of the series 3+ 8+22+72+266+ 103+ ........is divisi...

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  16. For the series 2+12+36+80+150+252 +….., the value of lim(n to oo) T/(n...

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  17. Statement 1 : If a+2b+3c=1 and a gt 0 , b gt 0 , c gt 0 then the gre...

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  18. For the series 21,22,23 ,…. K - 1 , k the A.M and G.M of the first ...

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  19. A sequence a(1),a(2), …..a(n)of real numbers is such that a(1) = 0 ,|a...

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  20. Let x(1),x(2),x(3)…..,x(n) be a sequence of integers such that -1 le x...

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