My borther needs help with this problem

Determine if the sequence is geometric. if it is, find the common ratio. 1) -2, 2/3, -2/9, 2/27 2) 0,2,5,9 3) 2, -10, 50, -250 4) 1,4,16,64

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Koji is installing a rectangular window in an office building. the window is 823 feet wide and 534 feet high. the formula for the area of a rectangle is a=bh. what is the area of the window? enter your answer as a mixed number in simplest form in the box. $$ ft2