Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence.
a1 = –4, a2 = 8, a3 = –16
The common ratio between consecutive terms in a geometric sequence is constant. To find it, we can divide any term by the previous term. For example:
r = a2/a1 = 8/(-4) = -2
We get a negative value for r, which means that the sequence alternates between positive and negative terms. The explicit formula for a geometric sequence is:
an = a1 * r^(n-1)
Substituting the given values, we get:
an = -4 * (-2)^(n-1)
To find the fifth term, we plug in n=5:
a5 = -4 * (-2)^(5-1) = -4 * 16 = -64
Therefore, the fifth term in the sequence is -64.