Answer :

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]