Final answer:
The explicit equation for the nth term of the sequence 1, 4, 16, 64 is an = 4^(n-1), as it follows the pattern of a geometric sequence with a common ratio of 4.
Step-by-step explanation:
The sequence given is 1, 4, 16, 64, which can be observed as a geometric sequence where each term is the result of the previous term multiplied by 4.
To find an explicit equation for the nth term of this sequence, we can use the general formula for the nth term of a geometric sequence: an = a1 × r¹(n-1), where a1 is the first term and r is the common ratio.
In this sequence, a1 is 1 and r is 4, leading us to the formula: an = 1 × 4¹(n-1) or simply an = 4¹(n-1).