Final answer:
The explicit equation for the geometric sequence 144, 24, 4, 2/3 is An = 144 * (1/6)^(n-1), where An represents the nth term of the sequence.
Step-by-step explanation:
The question asks to find the explicit equation for the given geometric sequence: 144, 24, 4, 2/3. An explicit equation for a geometric sequence is usually given by An = A1 * r^(n-1), where An is the nth term, A1 is the first term, r is the common ratio, and n is the term number.
To find the common ratio (r), we divide the second term by the first term: r = 24/144 = 1/6. Now that we have the common ratio, we can write the explicit equation for this geometric sequence as An = 144 * (1/6)^(n-1).