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The sum of first n terms of the series 3...

The sum of first n terms of the series `3.1 + 2^(2) + 3.3^(2) + 4^(2)+…` is `(n (n + 1) (4n - 1))/(6)` when n is even. The sum of first n terms when n is odd is

A

`(1)/(6) n (n + 1) (4n + 1)`

B

`(1)/(6) n(n + 1) (4n + 3)`

C

`(1)/(6) n(n + 1) (4n + 5)`

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)
  1. If a,b, and c are in G.P then a+b,2b and b+ c are in

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  2. The sum of first n terms of the series 1^(2) + 2.2^(2) + 3^(2) + 2.4^(...

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  3. The sum of first n terms of the series 3.1 + 2^(2) + 3.3^(2) + 4^(2)+…...

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  4. 1. If x ,y and z are respectively the p(th), q(th), and r(th) terms, r...

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  5. A.G.P. and H.P. have the same pth, qth and rth terms as a, b, c respec...

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  6. If x ,ya n dz are in A.P., a x ,b y ,a n dc z in G.P. and a ,b ,c in H...

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  7. Suppose a, b, c are in A.P. and a^(2), b^(2), c^(2) are in G.P. If a l...

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  8. If x, y, z are in A.P. then xth, yth and zth terms of any G.P. are in

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  9. If T(p), T(q), T(r) of an A.P. (G.P. or H.P.) are in A.P. (G.P. or H.P...

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  10. If x, y, z, w in N be four consecutive terms of an A.P., then T(x), T(...

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  11. If in any progressin the difference of any two consecutive terms bears...

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  12. In any progression, if (t(2)t(3))/(t(1)t(4)) = (t(2) + t(3))/(t(1) + t...

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  13. In a certain progression, three consecutive terms are 30, 24, 20. Then...

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  14. If (m + 1)th, (n + 1)th and (r + 1)th terms of an A.P. are in G.P. and...

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  15. If cos (theta - alpha), cos theta, cos (theta + alpha) are in H.P. the...

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  16. If A = lim(n rarr oo) sum(r = 1)^(n) tan^(-1) ((1)/(2r^(2))), then A i...

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  17. If S(n) = sum(r=1)^(n) (2r+1)/(r^(4) + 2r^(3) + r^(2)),"then S"(20) =

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  18. sum(r = 1)^(10) (r)/(1 - 3r^(2) + r^(4))=

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  19. If A = underset(n rarr oo)("Lt") sum(r = 1)^(n) tan^(-1) ((2r)/(2 + r^...

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  20. sum(r = 1)^(50) [(1)/(49 + r) - (1)/(2r(2r - 1))]=

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