Help me with both of these problems pl

Will give brainliest sum of arithmetic series (sigma notation) find the numerical answer to the summation given below. (image shown below)

Marquise has 200 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width w w (in meters) is modeled by: a ( w ) = − w 2 + 1 0 0 w a(w)=−w 2 +100w what side width will produce the maximum garden area? meters

Can anyone with some algebra 1 homework? : )