A certain song with 8 verses is played at a different tempo in each verse. The recursion below defines the sequence an , the song's tempo (in beats per minute) in the n^th verse.

Question

Which function represents the n^th term of this sequence, for n= 1,2,3,4,...8?

Answer 1

The function that represents the nth term of this sequence is:

a_n = f(n)

Where f(n) is a piecewise function defined as follows:

f(n) =
- 120 + 10n for n = 1
- 100 + 10n for n = 2
- 80 + 10n for n = 3
- 60 + 10n for n = 4
- 40 + 10n for n = 5
- 20 + 10n for n = 6
10n for n = 7
20n for n = 8

This function defines the tempo (in beats per minute) of each verse in the song.