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If a(n)=3-4n, then show that a(1),a(2),a...

If `a_(n)=3-4n`, then show that `a_(1),a_(2),a_(3), …` form an AP. Also, find `S_(20)`.

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If the sequence a_(1),a_(2),a_(3),dots a_(n),.... forms an A.P.then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)+...+a_(4)^(2)=(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If a_1,a_2,a_3,……..a_n, a_(n+1),…….. be A.P. whose common difference is d and S_1=a_1+a_2+……..+a_n, S_2=a_(n+1)+………..+a_(2n), S_3=a_(2n+1)+…………+a_(3n) etc show that S_1,S_2,S_3, S_4………… are in A.P. whose common difference is n^2d .

For the A.P., a_(1),a_(2),a_(3) ,…………… if (a_(4))/(a_(7))=2/3 , find (a_(6))/(a_(8))

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Let the sequence a_(1),a_(2),a_(3),...,a_(n) from an A.P.Then the value of a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-...+a_(2n-1)^(2)-a_(2n)^(2) is (2n)/(n-1)(a_(2n)^(2)-a_(1)^(2))(b)(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))(n)/(n+1)(a_(1)^(2)-a_(2n)^(2))(d)(n)/(n-1)(a_(1)^(2)+a_(2n)^(2))

If a_(m) be the mth term of an AP, show that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+"...."+a_(2n-1)^(2)-a_(2n)^(2)=(n)/((2n-1))(a_(1)^(2)-a_(2n)^(2)) .

OSWAL PUBLICATION-ARITHMETIC PROGRESSIONS -NCERT EXAMPLAR (EXERCISE-5.3)
  1. How many numbers lie between 10 and 300, which divided by 4 leave a re...

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  2. Find the sum of two middle terms of the AP -4/3,-1,-2/3,-1/3,...,4(1/3...

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  3. The first term of an AP is -5 and the last term is 45. If the sum of t...

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  4. Find the sum : 1+1.2+1.4+1.6+1.8+... (upto 21 terms)

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  5. Find: (4-1/n)+(7-2/n) +(10-3/n) ... upto n terms

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  6. Find the sum (i) 1+(-2)+(-5)+(-8)+ … +(-236) (ii) (4-(1)/(n))+(4-(...

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  7. Which term of the AP -2,-7,-12, … will be -77 ? Find the sum of this A...

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  8. If a(n)=3-4n, then show that a(1),a(2),a(3), … form an AP. Also, find ...

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  9. In an AP, If S(n)=n(4n+1), then find the AP.

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  10. In an AP, If S(n)=3n^(2)+5n and a(k)=164, then find the value of k.

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  11. If Sn denotes the sum of first n terms of an A.P., prove that S(...

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  12. Find the sum of first 17 terms of an AP whose 4th and 9th terms are -1...

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  13. If sum of first 6 terms of an AP is 36 and that of the first 16 terms ...

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  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

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  15. Find the sum of last ten terms of the AP 8, 10, 12, …, 126.

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  16. Find the sum of first seven numbers which are multiples of 2 as well a...

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  17. How many terms of the AP -15, -13, -11, … are needed to make the sun ...

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  18. The sum of the first n terms of an AP whose first term is 8 and the co...

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  19. Kanika was given her pocket money on Jan 1st , 2008. She puts Rs. 1 on...

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  20. Yasmeen saves Rs. 32 during the first month, Rs. 36 in the second mont...

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