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A sequence a(1),a(2), …..a(n)of real num...

A sequence `a_(1),a_(2), …..a_(n)`of real numbers is such that `a_(1) = 0 ,|a_(2)|=|a_(1)-2|,|a_(3)|=|a_(2)-2|,---|a_(n)| = |a_(n-1)-2|` . Then the maximum value of the arithmetic mean of these numbers is _____.

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The correct Answer is:
`rArr (a_(1)+a_(2)+....+a_(n))/n le 1 `
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FIITJEE-PROGRESSION & SERIES -SOLVED PROBLEMS (OBJECTIVE)
  1. 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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  2. If ar>0, r in N and a1.a2,....a(2n) are in A.P then (a1+a2)/(sqrta1+sq...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If a = sum(r=1)^(oo) 1/(r^(2)), b = sum(r=1)^(oo) 1/((2r-1)^(2)), th...

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  20. For 0 le theta ltpi/4, let x = sum(n=0)^(oo)(sin theta )^(2n), y = su...

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