Question 1190712
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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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<pre>
In arithmetic progression, if {{{a[1]}}}  is the first term and d is the common difference,
then the n-th term is

    {{{a[n]}}} = {{{a[1]}}} + (n-1)*d.


Memorize this general formula (!)


So, for the given progression

    {{{a[6]}}} = {{{-5}}} + {{{ (6-1)*(-5/6)}}} = {{{-5}}} + {{{5*(-5/6)}}} = {{{-5}}} - {{{25/6}}} = -5 - 4 {{{1/4}}} = -9 {{{1/6}}}.

    {{{a[n]}}} = {{{-5}}} + {{{(n-1)*(-5/6)}}} = {{{-5}}} - {{{(5(n-1))/6}}}.
</pre>

Solved.


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For introductory lessons on arithmetic progressions see 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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



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.