Using an arithmetic sequence, it is found that the smallest possible sum for the series is of 20 736, given by option B.
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- In an arithmetic sequence, the difference of consecutive terms is always the same, called common difference.
- The nth term of an arithmetic sequence is given by:

- The sum of the first n terms is given by:

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- The set of odd integers is an arithmetic sequence with common difference 2, thus
. - 384 terms, thus

- The last term is:

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The sum of the 384 terms is:

Now, for each option, we have to test if it generates an odd
.
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Option d: Sum of 1296, thus,
, solve for 



Not an integer, so not the answer.
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Option c: Test for 10000.



Not an integer, so not the answer.
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Option b: Test for 20736.



Integer an odd, thus, option b is the answer.
A similar problem is given at brainly.com/question/16720434