Question 1086131
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How to find the sum of the first 10 terms of each arithmetic sequence?

 1. a(sub1) = 11 and a(sub10) = 38

 2. a (sub1) = 10 and a(sub10) = 55
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<pre>
1.  Use the formula for the sum of an arithmetic progression

    {{{S[n]}}} = {{{((a[1]+a[n])/2)*n}}}:   {{{S[10]} = {{{((a[1]+a[10])/2)*10}}} = {{{((11+38)/2)*10}}} = {{{(49/2)*10}}} = 24.5*10 = 245.

    You do not need to calculate the common difference in this case.



2.  Do <U>THE SAME</U>:

    {{{S[n]}}} = {{{((a[1]+a[n])/2)*n}}}:   {{{S[10]}}} = {{{((a[1]+a[10])/2)*10}}} = {{{((10+55)/2)*10}}} = {{{(65/2)*10}}} = 32.5*10 = 325.

    Again, you do not need to calculate the common difference in this case.
</pre>


See introductory lessons on arithmetic progressions in this site

&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>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/One-characteristic-property-of-arithmetic-progressions.lesson>One characteristic property of arithmetic progressions</A>

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


The lessons marked (*) contain the formulas to sum arithmetic progression: read them very attentively.


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>.