The general rule would be
[tex]a_n=6-5(n-1)[/tex]
We first find the common difference, the value that is added every time to find the next term. This is the same as the slope; the formula for slope is
m=(y₂-y₁)/(x₂-x₁)
Letting x be the term number and y be the term value, we have
m=(-29--4)/(8-3) = (-29+4)/(8-3) = -25/5 = -5
Now we work backwards from a₃ to find a₁, the first term. We know that the common difference is -5; that means each time, the next term is found by subtracting 5. If we want to work backward we will add 5:
-4+5=1 for a₂
1+5=6 for a₁
Now we can write the general form:
[tex]a_n=6-5(n-1)[/tex]
