Answer:
The recursive formula is
\(f(1)=7\)
\(f(n)=f(n-1)+6\)
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
\(f(n)= f(n-1)+7\)
Where \(f(n)\) is the value of nth term of the sequence.
The sequence starts at 7, therefore the first term in the sequence is:
\(f(1)=7\)
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:
\(f(6)=f(5)+6=31+6=37.\).
Thus the next term in the sequence is 37, and the recursive formula is
\(f(1)=7\)
\(f(n)=f(n-1)+6.\)
