Answer:
The recursive formula is
[tex]f(1)=7[/tex]
[tex]f(n)=f(n-1)+6[/tex]
and the next term is in the sequence is 37.
Step-by-step explanation:
We first have to find a pattern in the numbers we are given. We notice that each number is 6 greater than the previous; for example 13 is 7+6, 19 is 13+6 and so on. Mathematically we write this as
[tex]f(n)= f(n-1)+7[/tex]
Where [tex]f(n)[/tex] is the value of nth term of the sequence.
The sequence starts at 7, therefore the first term in the sequence is:
[tex]f(1)=7[/tex]
Now the next term (it will be 6th term) of the sequence will be 6 greater than the previous term, and since the previous term is 31, we have:
[tex]f(6)=f(5)+6=31+6=37.[/tex].
Thus the next term in the sequence is 37, and the recursive formula is
[tex]f(1)=7[/tex]
[tex]f(n)=f(n-1)+6.[/tex]
