Sequences
We first compare the two first terms: 80, -20
We want to know how we can obtain the second term (-20) out of the first (80)
we know that there two ways at least:
-20 = 80 - 100
-20 = 80/(-4)
Now we compare the second and third term: -20, 5
Again, we want to know how we can obtain the third term (5) out of the second (-20):
5 = -20 + 35
5 = -20/(-4)
Then, we have the same way of obtaining a term: dividing the previous number by -4. Then the sequence is:
a₁ = 80
a₂ = 80/(-4) = -20
a₃ = -20/(-4) = 5
a₄ = 5/(-4) = -1.25
... etc
Then
aₙ = aₙ ₋ ₁ / (-4)
is the formula of the sequence