Write the explicit formula for the geometric sequence. Then find the fifth term in sequence.
a1 = -4, a2 = 8, a3 = -16
a. an = -4 * (2)^n; -64
b. an = -4 * (-2)^n-1; -64
c. an = -4 * (-2)^n; 128
d. an = -4 * (-2)^n-1; -512
The correct answer is b. an = -4 * (-2)^(n-1)
To find the explicit formula for a geometric sequence, we need to determine the common ratio (r) first. We can find the common ratio by dividing any term by its previous term.
r = a2/a1 = 8/(-4) = -2
Now we can substitute the values of a1, r, and n into the general formula:
an = a1 * r^(n-1)
an = -4 * (-2)^(n-1)
To find the fifth term in the sequence (a5), we substitute n = 5 into the formula:
a5 = -4 * (-2)^(5-1)
a5 = -4 * (-2)^4
a5 = -4 * 16
a5 = -64
Therefore, the fifth term in the sequence is -64, which matches option b.