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Answer:
410
Step-by-step explanation:
We are evaluating the sum:
[tex]\displaystyle \sum_{k\,=\,2}^{6} (90-2k)[/tex]
The summation notation means we increment k by 1 each time we plug k into the term definition and add them together:
[tex]\displaystyle \sum_{k\,=\,2}^{6} (90-2k) = (90-2(2)) + (90-2(3)) + (90-2(4)) + (90 - 2(5)) + (90-2(6))[/tex]
We can simplify this expression by grouping the 90s and applying the distributive property:
[tex]= 5(90) - 2(2 + 3 + 4 + 5 + 6)[/tex]
[tex]= 450 - 2(20)[/tex]
[tex]= 450 - 40[/tex]
[tex]\boxed{=410}[/tex]