The terms of the sequence are 14, 11, 8, 5, .....
Since
11 - 14 = -3
8 - 11 = -3
5 - 8 = -3
there is a constant difference between each two consecutive terms
then the sequence is an arithmetic sequence
The next five terms are
5 + -3 = 2
2 + -3 = -1
-1 + -3 = -4
-4 + -3 = -7
-7 + -3 = -10
The next five terms are
2, -1, -4, -7, -10
The explicit formula is
an is any term in the sequence
a is the first term
d is the constant difference
n is the position of the number
a = 14
d = -3
Multiply -3 by the bracket
an = 14 + (-3)(n) - (-3)(1)
an = 14 - 3n + 3
Add the like terms
an = 17 - 3n
The explicit formula is an = 17 - 3n
The recursive formula is
First-term = 14, an = an-1 + d
First term = 14; an = an-1 + (-3)