Question 1151680
.


            From the post by  @rfer you may conclude that the answer is  "at the  9-th year".


            But do not hurry --- it would be wrong (!)


            Read my solution below.



<pre>
You start count that income from the first year:


    {{{a[1]}}},  {{{a[2]}}}, {{{a[3]}}}, . . . , {{{a[n]}}}.


The first term of this sequence is $19900.


It is <U>arithmetic sequence</U>, and its common difference is 1300, as @rfer correctly determined in his post.


Therefore, you can write 


    {{{a[n]}}} = 1300 + (n-1)*1300.


You want to find "n" in a way that


    31600 = 1300 + (n-1)*1300.


It gives you


    n - 1 = {{{(31600-19900)/1300}}} = {{{11700/1300}}} = 9.


    Hence,  n = 9+1 = 10.


<U>ANSWER</U>.  "At which year ?"  ----  at the 10-th year.
</pre>

So, &nbsp;the correct answer is &nbsp;"at the &nbsp;10-th year";  &nbsp;or &nbsp;9 &nbsp;years &nbsp;<U>after</U> &nbsp;the &nbsp;1-st year.


Solved.


From my post learn that not only calculations, &nbsp;but the entire conception of the solution and the answer itself 
should be presented accurately -- if you want high scores.



------------------


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.