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?
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.