Final answer:
The explicit formula for the nth term of the sequence 4, -24, 144, .... is an = 4 * (-6)^(n-1).
Step-by-step explanation:
The given sequence is 4, -24, 144, ....
To find the explicit formula for the nth term of the sequence, we can observe that each term is obtained by multiplying the previous term by -6. The first term is 4, so the explicit formula can be written as:
an = 4 * (-6)^(n-1)
For example, the fourth term (n = 4) would be:
a4 = 4 * (-6)^(4-1) = 4 * (-6)^3 = 4 * -216 = -864