Question 1026097
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Write the sum using summation notation, assuming the suggested pattern continues.

-4 + 5 + 14 + 23 + ... + 131 
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-4 + 5 + 14 + 23 + ... + 131 = {{{ sum ((-4 + (k-1)*9), k=1, 16 ) }}}.


This is the sum of the first 16 terms of an arithmetic progression with the first term -4 and the common difference 9.


The last term is 16-th (at k = 16), and it is equal to -4 + (16-1)*9 = -4 + 15*9 = 131.


On arithmetic progressions see the lesson <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A> in this site, and the lessons associated with it.
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<U>comment from student</U>: Thanks! I have one last question: Write the sum using summation notation, assuming 
the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81. 



<U>My response</U>:
<pre>
-9 - 3 + 3 + 9 + ... + 81 = {{{ sum ((-9 + (k-1)*6), k=1, 16 ) }}}.


This is the sum of the first 16 terms of an arithmetic progression with the first term -9 and the common difference 6.


The last term is 16-th (at k = 16), and it is equal to -9 + (16-1)*6 = -9 + 15*6 = 81.
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