Question

Josh made his school basketball team this year. He played 10 minutes in his first game, but he played twice that amount in each of the other games. Let y represent the total number of minutes Josh played in x games.

Which type of sequence does the situation represent?

A.
The situation represents an arithmetic sequence because the successive values have a common difference of 10.
B.
The situation represents an arithmetic sequence because the successive values have a common difference of 20.
C.
The situation represents a geometric sequence because the successive values have a common ratio of 2.
D.
The situation represents a geometric sequence because the successive values have a common ratio of 5.

Answer 1

B. The situation represents an arithmetic sequence because the successive values have a common difference of 20.

Explanation:

(x, y) values appear to be ...

(1, 10) . . . . 10 minutes played in the first game

(2, 30) . . . 20 minutes played in the second game, adding 20 to the total

(3, 50) . . . 20 minutes played in the third game, adding 20 to the total

From here, we can see that each additional game adds 20 minutes to the total (y), so the sequence is ...

an arithmetic sequence because the successive values have a common difference of 20