Question 1196342
.
Find the sum of the 1st 20 terms of the arithmetic sequence
-2, -5, -8, -11.
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<pre>
First term is  {{{a[1]}}} = -2.

The common difference is  d = (-5) - (-2) = -5 + 2 = -3.


Use the formula for the sum of the first n term of an arithmetic progression

    {{{S[n]}}} = {{{((a[1] + a[n])/2)*n}}}.


You need to know the 20th term  {{{a[20]}}}. It is (use the formula for the n-th term)

    {{{a[20]}}} = {{{a[1] + (20-1)*d}}} = -2 + 19*(-3) = -59.


Therefore,  {{{S[20]}}} = {{{((-2) + (-59))/2)*20}}} = {{{((-61)/2)*20}}} = {{{(-61)*10}}} = -610.


<U>ANSWER</U>.  The sum of the first 20 terms of this AP is  -610.
</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.