A certain song with 8 verses is played at a different tempo in each verse. The recursion below defines the sequence , the song's tempo (in beats per minute) in the verse.
a1 = 50
an =an-1+12
Which function represents the term of this sequence, for n=1,2,3,4....8 ?
A.
B.
C.
The recursive formula indicates that each term in the sequence is 12 more than the previous term. We can use this information to find the value of the 8th term, a8.
Starting with a1 = 50, we can use the recursive formula to find the values of a2, a3, a4, ..., a8:
a2 = a1 + 12 = 50 + 12 = 62
a3 = a2 + 12 = 62 + 12 = 74
a4 = a3 + 12 = 74 + 12 = 86
a5 = a4 + 12 = 86 + 12 = 98
a6 = a5 + 12 = 98 + 12 = 110
a7 = a6 + 12 = 110 + 12 = 122
a8 = a7 + 12 = 122 + 12 = 134
Therefore, the 8th term of the sequence is 134.
To find the function that represents the nth term of the sequence, we can observe that each term is 12 more than the previous term. This can be represented with the function:
f(n) = 50 + 12(n-1)
Therefore, the correct function that represents the nth term of the sequence, for n=1,2,3,4....8, is:
C.