Let `A_1 , G_1, H_1`denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For `n >2,`let `A_(n-1),G_(n-1)` and `H_(n-1)` has arithmetic, geometric and harmonic means as `A_n, G_N, H_N,` respectively.A. `G_(1)gtG_(2)gtG_(3)gt"......."`B. `G_(1)ltG_(2)ltG_(3)lt"......."`C. `G_(1)=G_(2)=G_(3)="......."`D. `G_(1)ltG_(3)ltG_(5)lt"......." and "G_(2)gtG_(4)gtG_(6)gt"......."`

Let `A_1 , G_1, H_1`denote the arithmetic, geometric and harmonic mean

1.	Let `A_1 , G_1, H_1`denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For `n >2,`let `A_(n-1),G_(n-1)` and `H_(n-1)` has arithmetic, geometric and harmonic means as `A_n, G_N, H_N,` respectively.A. `G_(1)gtG_(2)gtG_(3)gt"......."`B. `G_(1)ltG_(2)ltG_(3)lt"......."`C. `G_(1)=G_(2)=G_(3)="......."`D. `G_(1)ltG_(3)ltG_(5)lt"......." and "G_(2)gtG_(4)gtG_(6)gt"......."`
Answer» Correct Answer - C `A_(1)=(a+b)/(2),G_(1)=sqrt(ab),H_(1)=(2ab)/(a+b)` `A_(n)=(A_(n-1)+H_(n-1))/(2),G_(n)=sqrt(A_(n-1)H_(n-1))" and " H_(n)=(2A_(n-1)H_(n-1))/(A_(n-1)+H_(n-1))` Clearly, `G_(1)=G_(2)=G_(3)="......"=sqrt(ab)`.

Discussion

No Comment Found

Related InterviewSolutions

Let `S_(n)` denote the sum of n terms of the series `1^(2)+3xx2^(2)+3^(2)+3xx4^(2)+5^(2)+3xx6^(2)+7^(2)+ . . . .` Statement -1: If n is odd, then `S_(n)=(n(n+1)(4n-1))/(6)` Statement -2: If n is even, then `S_(n)=(n(n+1)(4n+5))/(6)`A. Statement -1 is true, Statement -2 is True, Statement -2 is a correct explanation for Statement for Statement -1.B. Statement -1 is true, Statement -2 is True, Statement -2 is not a correct explanation for Statement for Statement -1.C. Statement -1 is true, Statement -2 is False.D. Statement -1 is False, Statement -2 is True.
The odd value of n for which `704 + 1/2 (704) + 1/4 (704) + ... upto n terms = 1984 - 1/2 (1984) + 1/4 ( 1984) - .... upto n terms is :A. 5B. 3C. 4D. 10
The positive integer `n`for which `2xx2^2xx+3xx2^3+4xx2^4++nxx2^n=2^(n+10)`is`510`b. `511`c. `512`d. 513A. 510B. 512C. 513D. 508
If the first two terms of a H.P. are `2//5and12//23` respectively. Then, largest term isA. 5th termB. 6th termC. 4th termD. 6th term
consider an infinite geometric series with first term `a` and comman ratio `r` if the sum is `4` and the second term is `3/4` then find `a&r`A. `a = 4//7, r= 3//7`B. `a = 2, r = 3//8`C. `a = 3//2, r = 1//2`D. `a = 3, r =1//4`
If `1^2+2^2+3^2++2003^2=(2003)(4007)(334)a n d(1)(2003)+(2)(2002)+(3)(2001)++(2003)(1)=(2003)(334)(x),t h e nx`equals`2005`b. `2004`c. `2003`d. 2001A. 2005B. 2004C. 2003D. 2001
Find the sum of the series `1+2^(2)x+3^(2)x^(2)+4^(2)x^(3)+"...."" upto "infty|x|lt1`.
If the two terms of a H.P. are `2//5and12//23` respectively, then the largest term isA. 6B. 12C. 5D. 7
Let a,b,c be in A.P. and `|a|lt1,|b|lt1|c|lt1.ifx=1+a+a^(2)+ . . . ."to "oo,y=1+b+b^(2)+ . . . ."to "ooand,z=1+c+c^(2)+ . . . "to "oo`, then x,y,z are inA. APB. GPC. HPD. none of these
An infinite GP has first term `x`and sum 5, then `x`belongs to(2004, 1M)`x

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment