SOLUTION: Hi I need help finding the first term of an Arithmetic Series with the given info. My common difference is 6 My Sn is 574 My N is 14 The answer according to my text book

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Question 782245: Hi I need help finding the first term of an Arithmetic Series with the given info.
My common difference is 6
My Sn is 574
My N is 14
The answer according to my text book is 2 can you help me?
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Hi I need help finding the first term of an Arithmetic Series with the given info.
My common difference is 6
My Sn is 574
My N is 14
The answer according to my text book is 2 can you help me?

The sum of an arithmetic series is: S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29, with:

S%5Bn%5D given as: 574; n given as: 14; a%5B1%5D NOT GIVEN; and d, or common difference given as: 6

Therefore, S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29 becomes: 574+=+%2814%2F2%29%282a%5B1%5D+%2B+%2814+-+1%296%29

574+=+7%282a%5B1%5D+%2B+%2813%296%29

574+=+7%282a%5B1%5D+%2B+78%29

574+=+14a%5B1%5D+%2B+546

14a%5B1%5D+=+574+-+546
14a%5B1%5D+=+28

The 1st term, or a%5B1%5D = 28%2F14, or highlight_green%282%29