Question 1047092
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hi I am learning pre-calculus 11 and am stuck on this question thank you! 

Q. Determine the sum, Sn, for each arithmetic sequence described.
a) T1=7, Tn=79, n=8 

they do not tell me what D is, so I am confused.. :)
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<pre>
There are two formulas for the sum of an arithmetic progression.

The first formula is 

    {{{S[n]}}} = {{{T[1] + T[2] + T[3] + ellipsis + T[n]}}} = {{{(T[1] + (n-1)*d/2)*n}}}. 


It really requires to know the "d", the common difference.


But there is another formula for the sum of an arithmetic progression:

    {{{S[n]}}} = {{{((T[1] + T[n])/2)*n}}}. 

for which to know {{{T[1]}}},  {{{T[n]}}}  and  n  is enough.


So, use this second formula, and you get


    {{{S[8]}}} = {{{((T[1] + T[8])/2)*8}}} = {{{((7+79)/2)*8}}} = 344.
</pre>

For arithmetic progressions, see the lessons 

&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=http://www.algebra.com/algebra/homework/Sequences-and-series/Chocolate-bars-and-arithmetic-progressions.lesson>Chocolate bars and arithmetic progressions</A>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/One-characteristic-property-of-arithmetic-progressions.lesson>One characteristic property of arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-for-sequences-other-than-arithmetic-or-geometric.lesson>Mathematical induction for sequences other than arithmetic or geometric</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Proving-inequalities-by-the-method-of-Mathematical-Induction.lesson>Proving inequalities by the method of Mathematical Induction</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> 


OVERVIEW of my lessons on arithmetic progressions with short annotations is in the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Review-of-lessons-on-arithmetic-progressions.lesson>OVERVIEW of lessons on arithmetic progressions</A>.