Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence.
a1 = -4, a2 = 8, a3 = -16
The explicit formula for a geometric sequence is given by the formula
an = a1 * r^(n-1)
where a1 is the first term and r is the common ratio.
In this case, we have a1 = -4 and a2 = 8. Therefore, we can find the common ratio, r, by dividing a2 by a1:
r = a2 / a1
= 8 / (-4)
= -2
Now, we can use the explicit formula to find the fifth term (a5) in the sequence:
a5 = a1 * r^(5-1)
= -4 * (-2)^(4)
= -4 * 16
= -64
Therefore, the fifth term in the sequence is -64.