Sequence:

27, 22, 17, 12

Pattern:

current number less 5 to get next number.

nth Rule:

nth term = 32 - 5n

Proof of nth rule formula:

based on sequence,

if n=1, 1st term = 27

Let's try our formula,

nth term = 32 - 5n

1st term = 32 - 5(1)

1st term = 32 - 5

1st term = 27 ✔️✔️✔️ TRUE

based on sequence,

if n=4, 4th term = 12

Let's try our formula ,

nth term = 32 - 5n

4th term = 32 - 5(4)

4th term = 32 - 20

4th term = 12 ✔️✔️✔️ TRUE