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(i) 1,3,5,7,… (ii) pi,pi+e^(pi),pi+2e^...

(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. (i) 1,3,5,7,… (ii) pi,pi+e^(pi),pi+2e^(pi),"...." (iii) a, a-b, a-...

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  2. Let a, b, c be in A.P. and |a|lt1,|b|lt1|c|lt1. If x=1+a+a^(2)+ . . . ...

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  3. If an=3/4-(3/4)^2+(3/4)^3+...(-1)^(n-1)(3/4)^n and bn=1-an, then find ...

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  4. If a1, a2, a3, be terms of an A.P. if (a1+a2++ap)/(a1+a2++aq)=(p^2)/(...

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

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

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

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

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

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  12. in a geometric progression consisting of positive terms, each term eq...

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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 su...

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  15. If the sum of first n terms of an AP is cn^(2), then the sum of square...

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  16. 1+2/3+6/(3^2)+10/(3^3)+14/(3^4)+...oo=

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  17. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

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

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  19. A person is to cout 4500 currency notes. Let a(n) denotes the number o...

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

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  21. A man saves Rs. 200 in each of the first three months of his service. ...

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