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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` .
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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