SOLUTION: Write the sum using summation notation, assuming the suggested pattern continues. -4 + 5 + 14 + 23 + ... + 131

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Question 1026097: Write the sum using summation notation, assuming the suggested pattern continues.
-4 + 5 + 14 + 23 + ... + 131
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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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+%28%28-4+%2B+%28k-1%29%2A9%29%2C+k=1%2C+16+%29+.


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 Arithmetic progressions in this site, and the lessons associated with it.


comment from student: Thanks! I have one last question: Write the sum using summation notation, assuming
the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81.


My response:
-9 - 3 + 3 + 9 + ... + 81 = +sum+%28%28-9+%2B+%28k-1%29%2A6%29%2C+k=1%2C+16+%29+.


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.