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?

Answer 1

To find the equation for the nth term in the sequence, we can observe that the difference between consecutive terms is 4.

Since a3=0, we can determine the value of a1 by subtracting 2 from a3: a1 = a3 - 2 = 0 - 2 = -2.

Now, let's denote the equation for the nth term as an = pn + q, where p and q are constants to be determined.

To find the value of p, we can express the difference between consecutive terms:
a2 - a1 = (p(2) + q) - (p(1) + q) = p(2-1) = p
Since a2 - a1 = 4, we have: p = 4.

Now, let's substitute the value of p into the equation:
an = 4n + q.

To determine the value of q, we can substitute a4 into the equation:
a4 = 4(4) + q = 16.
Solving for q, we have: 16 - 16 = q, thus q = 0.

Therefore, the equation for the nth term in the sequence is: an = 4n.