SOLUTION: Find a_65 for the arithmetic sequence: 9,5,1,−3...

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Question 1161364: Find a_65 for the arithmetic sequence: 9,5,1,−3...
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The first term of this arithmetic progression is  a%5B1%5D = 9.


The common difference is  d = -4.


The general formula is


    a%5Bn%5D = a%5B1%5D+%2B+d%2A%28n-1%29.


In your case it takes the form


    a%5B65%5D = 9 - 4*(64-1).


You do the arithmetic.

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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.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Find a%5B65%5D for the arithmetic sequence:
9,5,{{1}}},-3..
a%5B1%5D+=9d=-4
a%5Bn%5D+=a%5B1%5D+%2Bd%28n-1%29
a%5Bn%5D+=9-4%28n-1%29
a%5B65%5D=9-4%2865-1%29
a%5B65%5D=9-4%2864%29
a%5B65%5D=9-256
a%5B65%5D=-247