In a sequence of numbers, a3=0, a4=4, a5=8, a6=12, and a7=16. Based on this information, which equation can be used to find the nth term in the sequence, an?

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