Describe the multiplication pattern and find the next two terms.

25; 100; 400; 1600; 6400; . .

a. the first term is 25. each term is multiplied by 5. the next 2 terms are 32,000 and 160,000.

b. the first term is 25. each term is multiplied by 4.
the next 2 terms are 25,600 and 102,400.

c. the first term is 25. each term is multiplied by 4.
the next 2 terms are 2560 and 10,240.

d. the first term is 25. each term is multiplied by 5.
the next 2 terms are 3200 and 16,000.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?