Answer: aₙ = -12 + 4*n
Step-by-step explanation:
We know that:
a₃ = 0
a₄ = 4
a₅ = 8
a₆ = 12
a₇ = 16
This seems to be an arithmetic sequence.
To test this, we need to calculate the difference between any two consecutive terms in the sequence, and this must be a constant for any pair that we choose.
a₄ - a₃ = 4 - 0 = 4
a₅ - a₄ = 8 - 4 = 4
a₆ - a₅ = 12 - 8 = 4
etc
we can conclude that this is an arithmetic sequence.
The n-th term in an arithmetic sequence, where the increase between consecutive terms is 4, is:
aₙ = aₙ₋₁ + 4.
Another way is:
aₙ = a₀ + n*4.
Where to find a₀, we can start with the value that we know and go back:
a₂ = a₃ - 4 = -4
a₁ = a₂ - 4 = -8
a₀ = a₁ - 4 = -12
Then the n-th term can be written as:
aₙ = -12 + 4*n
