Final answer:
The nth term of the sequence is given by the formula a_n = 3 × 2^(n-1). To find the 75th term, substitute 75 for n in the formula, resulting in a_75 = 3 × 2^74.
Step-by-step explanation:
The sequence provided {3, 6, 12, …} appears to be a geometric sequence where each term is multiplied by 2 to get the next term. This means that the sequence is defined by the formula a_n = a_1 × r^(n-1), where a_n is the nth term, a_1 is the first term (which is 3), and r is the common ratio (which is 2).
To find an explicit rule for the nth term (a_n), we can write this as a_n = 3 × 2^(n-1). To find the 75th term of the sequence (a_75), we would then plug in 75 for n: a_75 = 3 × 2^(75-1) = 3 × 2^74.
Without a calculator, we are unable to give the exact value of 2^74, but the explicit rule allows anyone with a calculator to easily find the exact value of any term in the sequence.