Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67

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21-07-2017
Mathematics

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Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67

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konrad509 konrad509 · Answer 1 · 2017-07-21T18:09:42+02:00

konrad509 konrad509

21-07-2017

[tex]a_1=-8\\ r=5\\ a_n=67\\\\ a_n=a_1+(n-1)r\\ 67=-8+(n-1)\cdot5\\ 67=-8+5n-5\\ 5n=80\\ n=16\\\\ \displaystyle \sum_{i=1}^{16}(-8+(n-1)\cdot5)=\sum_{i=1}^{16}(-8+5n-5)=\boxed{\sum_{i=1}^{16}(5n-13)}[/tex]

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