<PRE><B>Question 1151584</B>
.


&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;I will solve and answer parts &amp;nbsp;(a), &amp;nbsp;(b) &amp;nbsp;and &amp;nbsp;(c) &amp;nbsp;only.



&lt;pre&gt;
a)  is the arithmetic progression with the first term 1 and the common difference of 4.

    {{{a[n]}}} = 1 + 4*(n-1) = 4n - 3.



b)  is the arithmetic progression with the first term 70 and the common difference of 50.

    {{{a[n]}}} = 70 + 50*(n-1) = 50n + 20.



c)  is the geometric progression with the first term 1 and the common ratio of 3.

    {{{a[n]}}} = {{{1*3^(n-1)}}} = {{{3^(n-1)}}}.
&lt;/pre&gt;


I just opened your eyes  --- you do the rest.


----------------


This problem is about the &amp;nbsp;SIMPLEST &amp;nbsp;properties of arithmetic and geometric progressions.


Learn the subjects from these two groups of &amp;nbsp;&lt;U&gt;introductory&lt;/U&gt; &amp;nbsp;lessons in this site


&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson&gt;Arithmetic progressions&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson&gt;The proofs of the formulas for arithmetic progressions&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson&gt;Problems on arithmetic progressions&lt;/A&gt;  

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson&gt;Word problems on arithmetic progressions&lt;/A&gt;


and


&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson&gt;Geometric progressions&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-geometric-progressions.lesson&gt;The proofs of the formulas for geometric progressions&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-geometric-progressions.lesson&gt;Problems on geometric progressions&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-geometric-progressions.lesson&gt;Word problems on geometric progressions&lt;/A&gt;



Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-II - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lessons are the part of this online textbook under the topics &amp;nbsp;&lt;U&gt;&quot;Arithmetic progressions&quot;&lt;/U&gt; &amp;nbsp;and &amp;nbsp;&lt;U&gt;&quot;Geometric progressions&quot;&lt;/U&gt;.



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.


</PRE>