Question 1186348
.
<pre>

It is about finding the number of terms of an arithmetic progression, when its

first term, the common difference and the sum of n terms are given.


The formula for the sum of n first terms of an AP is


    {{{S[n]}}} = {{{(a[1] + (d*(n-1))/2)*n)}}},


In this problem,  {{{a[1]}}} = 10,  d = 6.  So your equation is


    {{{(10 + (6*(n-1))/2)*n}}} = 3920.


Multiply both sides by 2


    (20 + 6*(n-1))*n = 7840

    20n + 6n^2 - 6n = 7840

     6n^2 + 14n - 7840 = 0.


Apply the quadratic formula and find the roots.


You will get two roots. One root is negative, and we reject it.


The other root is positive, and its value is  35.


It is the solution to the problem.


<U>ANSWER</U>.  35 rows.
</pre>

Solved.


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


On geometric progressions, &nbsp;see introductory lessons

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

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

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

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