Find an explicit formula for the arithmetic sequence 12, 5, - 2, - 9, ...

an = 12 - 7 (n-1)

an = 19-7n

Step-by-step explanation:

The explicit formula for an arithmetic sequence is

an = a1 + d (n-1) where a1 is the first term and d is the common difference

a1 = 12

We find d by taking the second term and subtracting the first term

d = 5-12

d = - 7

an = 12 - 7 (n-1)

We can simplify this

an = 12 - 7n+7

an = 19-7n