Question 1128870
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<pre>
The condition immediately implies that the sum 

    {{{a[21]}}} + {{{a[22]}}} = 0.


Thus  {{{a[22]}}} = -{{{a[21]}}}.


From the other side,  {{{a[22]}}} = {{{a[21] + d}}} = {{{-a[22] + (-2)}}}.


It implies  {{{2*a[22]}}} = -2;  hence,  {{{a[22]}}} = -1.



From the other side,  {{{a[22]}}} = {{{a[1] + 21*d}}} = {{{a[1] + 21*(-2)}}} = {{{a[1] - 42}}}.


Hence,  {{{a[1]}}} = {{{a[22] + 42}}} = -1 + 42 = 41.


<U>Answer</U>.  {{{a[1]}}} = 41.
</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.