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There are 4n + 1 terms in a sequence of ...

There are `4n + 1` terms in a sequence of which first `2n + 1` are in Arithmetic Progression and last `2n + 1` are in Geometric Progression the common difference of Arithmetic Progression is `2` and common ratio of Geometric Progression is `1/2`. The middle term of the Arithmetic Progression is equal to middle term of Geometric Progression. Let middle term of the sequence is `T_m` and `T_m` is the sum of infinite Geometric Progression whose sum of first two terms is `(5/4)^2 n` and ratio of these terms is `9/16`.

1. Number of terms in the given sequence is equal to -
(a) 9
(b) 17
(c) 13
(d) none

2. Middle term of the given sequence, i.e. `T_m` is equal to
(a) 16/7
(b) 32/7
(c) 48/7
(d) 16/9

3. First term of given sequence is equal to -
(a) –8/7, –20/7
(b) –36/7
(c) 36/7
(d) 48/7

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
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  2. If S1,S2 and S3 be respectively the sum of n, 2n and 3n terms of a G.P...

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  3. There are 4n + 1 terms in a sequence of which first 2n + 1 are in Arit...

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  5. Find the sum of n terms of the series whose nth term is T(n)=tanx/(2^n...

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  6. Evaluate, sum(i = 0)^iinfty sum(j = 0)^infty sum(k = 0)^infty 1/(3^i c...

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  8. If log(2)(5.2^(x)+1),log(4)(2^(1-x)+1) and 1 are in A.P,then x equals

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  9. Find the geometric series whose 5th and 8th terms are 80 and 640 respe...

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  12. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

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  13. The 5th, 8th and 11th terms of a GP are a,b,c respectively. Show that...

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  14. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

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  15. If p be the first of n arithmetic means between two numbers and q be t...

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  16. Find the centre and radius of the circle: (x+5)^2+(y-3)^2=20

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  18. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

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  19. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

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