<h2>
Answer:</h2>
Recursive Formula: f(n)=f(n-1)+6
Explicit formula: f(n)= 6n+1
<h2>
Step-by-step explanation:</h2>
We are given a sequence of arithmetic progression as:
7 , 13 , 19 , 25
This means that the common difference of the sequence is: 6
( Since
13-7=6
19-13=6
and 25-19=6 )
This means that each term of the sequence is 6 more than that of the preceding term of the sequence.
i.e. the recursive formula for the sequence is given by:
f(n)=f(n-1)+6
Also, the general rule or the explicit function that describes this situation is:
f(n)=6n+1
( Since the first term of the sequence is calculated when n=1
f(1)=6×1+1=7
second term i.e. n=2
f(2)=6×2+1=13
f(3)=6×3+1=19
and so on )