Question 1047684
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The first two terms of an arithmetic sequence are 3, 7 and the last term is 355.

Thanks in advance for helping out! I understand the concept but am having difficulty in solving this problem. 
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First of all, the common difference is 4.


<pre>
a. How many terms are there?  - How many intervals of the length of 4 are there between 3 and 355? {{{(355-3)/4)}}} = {{{352/4}}} = 88.

                              - How many terms are there in between including endpoints? 88+1 = 89.


b. What is the 40th term?     - It is easy, and if you understand the concept, you must answer it. 
                                {{{a[40]}}} = {{{a[1] + (n-1)*d}}} = 3 +39*4 = calculate on your own.

c. What is the sum of the series?    {{{S[n]}}} = {{{((a[1]+a[n])/2)*n}}} = {{{((3 + 355)/2)*89}}} = calculate it on your own
</pre>


There is a bunch of lessons on arithmetic progression in this site.
The introductory level lessons are 

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