Reba is learning to play violin. Each month, Reba is able to play 2 times as many songs as she was able to play the month before. If you list the total number of songs that she can play each month, what kind of sequence will you see? arithmetic geometric both neither Submit

Answer 1

Reba's ability to play songs doubles each month. If she can play \( x \) songs in the first month, then in the second month she can play \( 2x \), in the third month \( 4x \), in the fourth month \( 8x \), and so on. The pattern of the number of songs is:

• Month 1: \( x \)
• Month 2: \( 2x \)
• Month 3: \( 4x \)
• Month 4: \( 8x \)

This can be represented as \( x \cdot 2^n \), where \( n \) is the month number starting from 0 (i.e., Month 1 corresponds to \( n = 0 \), Month 2 corresponds to \( n = 1 \), etc.).

This sequence is not arithmetic, because in an arithmetic sequence the difference between consecutive terms is constant, and here the ratios are constant (doubling).

This sequence is a geometric sequence because the ratio of successive terms is constant (each term is 2 times the previous term).

Thus, the answer is: geometric.