Sort the sequence according to whether they are arithmetic

Given a: b and b: c, find a: b: c. write the ratio in simplest form. a: b=6: 10 and b: c=21: 33

Timmy uses 1 1 2 cups of sugar for every 2 gallons of lemonade he makes. how many cups of sugar would timmy use if he makes 13 gallons of lemonade?

Which geometric principle is used to justify the construction below?