SOLUTION: in an arithmetic sequence, the first term is -5 and the common diffference is -5/6. What is the 6th term? the nth term?

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Question 1190712: in an arithmetic sequence, the first term is -5 and the common diffference is -5/6. What is the 6th term? the nth term?
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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in an arithmetic sequence, the first term is -5 and the common diffference is -5/6.
What is the 6th term? the nth term?
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In arithmetic progression, if a%5B1%5D  is the first term and d is the common difference,
then the n-th term is

    a%5Bn%5D = a%5B1%5D + (n-1)*d.


Memorize this general formula (!)


So, for the given progression

    a%5B6%5D = -5 + +%286-1%29%2A%28-5%2F6%29 = -5 + 5%2A%28-5%2F6%29 = -5 - 25%2F6 = -5 - 4 1%2F4 = -9 1%2F6.

    a%5Bn%5D = -5 + %28n-1%29%2A%28-5%2F6%29 = -5 - %285%28n-1%29%29%2F6.

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.