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Which of the following are A.P. (i) 1,3,...

Which of the following are A.P. (i) 1,3,5,7,…
(ii) `pi,pi+e^(pi),pi+2e^(pi),"...."`
(iii) `a, a-b, a-2b,a-3b,"…."`

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(i) Here, 2nd term - 1st term = 3rd term - 2nd term `="…."`
`implies 3-1=5-3="..."=2,` which is a common difference.
(ii) Here, 2nd term - 1st term = 3rd term -2nd term` ="…."`
`implies (pi+e^(pi))-pi=(pi+2e^(pi))-(pi+e^(pi))="...."`
`" "=e^(pi),` which is a common difference.
(iii) Here, 2n term -1st term = 3rd term -2nd term ="...."
`implies (a-b)-a=(a-2b)-(a-b)="...."`
`" "=-b,` which is a common difference.
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Which of the following are A.P. (i) 1,3,5,7,… (ii) pi,pi+e^(pi),pi+2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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