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Let a,b,c be in A.P. and |a|lt1,|b|lt1|c...

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 in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, `x=(1)/(1-a),y=(1)/(1-b)" and "z=(1)/(1-c)`
Since, a,b,c are in AP.
`implies 1-a,1-b,1-c` ,are also in AP.
`implies (1)/(1-a),(1)/(1-b),(1)/(1-c)` are in HP.
`:. X,y,z` are in HP.
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let a,b,c be in A.P. and |a|lt1,|b|lt1|c|lt1.ifx=1+a+a^(2)+ . . . ."to...

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  2. Evluate int (tan^(-1)x)/(1+x^2) dx

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  3. If a1, a2, a3, be terms of an A.P. and (a1+a2+.....+ap)/(a1+a2+.....+...

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  4. If a1, a2, a3,.....an are in H.P. and a1 a2+a2 a3+a3 a4+.......a(n-1...

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  5. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

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  6. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  7. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

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  8. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

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  9. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  10. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

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  11. In a G.P of positive terms if any term is equal to the sum of the next...

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  12. Suppose four distinct positive numbers a(1),a(2),a(3),a(4) are in G.P....

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  13. The first two terms of a geometric progression add up to 12. The sum o...

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  14. If the sum of first n terms of an A.P. is cn^(2) then the sum of squar...

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  15. The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

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  16. Let Sk,k=1, 2, …. 100 denote the sum of the infinite geometric series ...

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  17. Let a1, a2, a3, ,a(11) be real numbers satisfying a1=15 , 27-2a2>0 an...

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  18. Check 2,4,6,8,10 are in A.P or not

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  19. The minimum value of the sum of real numbers a^-5, a^-4, 3a^-3, 1,a^8 ...

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  20. A man saves ₹ 200 in each of the first three months of his servies.In ...

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