Question 1202439
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Calculate the sum of the series: - 396 - 308 - 220 - 132 - ... + 836.
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<pre>
The sequense  -396, -308, -220, -132, . . ., 836  is an arithmetic progression
with the first term  a= -396  and the common difference of d= 88  
(sinse -308 - (-396) = 88  and each next term is 88 units greater than the current term).


Find the number of term. Use the formula for the n-th term

    836 = -396 + 88*(n-1).


It gives  (836 + 396) = 88*(n-1);  n-1 = {{{(836+396)/88}}} = 14;  hence,  n= 15.

<U>CHECK</U>.  -396 + (15-1)*88 = use your calculator = 836,  correct.


To find the sum of this AP, use the general formula for the sum of an AP

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


It gives at n= 15

    {{{S[15]}}} = {{{((-396+836)/2)*15}}} = use your calculator = 3300.   <U>ANSWER</U>
</pre>

Solved.


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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.



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