Question

What is the explicit formula for the sequence 7,2,-3,-8,-13

Answer 1

You could say that      a(n) = 12 - 5n .

Then ...

a(1) = 12 - 5 = 7
a(2) = 12 - 10 = 2
a(3) = 12 - 15 = -3
and so on.
So it seems to work.

Answer 2

7, 2, -3, -8, -13
 -5  -5  -5  -5

a(n) = a₁ + d(n - 1)
a(n) = 7 - 5(n - 1)
a(n) = 7 - 5(n) + 5(1)
a(n) = 7 - 5n + 5
a(n) = -5n + 7 + 5
a(n) = -5n + 12