Help me please this is on writing direct proportions but I don’t really understand it

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

Pls! does anybody know a shortcut for answering these types of questions in the future?

Suzanne began a trip with 18 1/2 gallons of gas in the gas tank of her car if she hughes 17 3/4 gallons on the trip how many gallons does she have left once she finish the trip