If the pattern below follows the rule "starting with five, every consecutive line
has a number one more than the previous line," how many marbles must be in
the seventh line?

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?