Final answer:
To find the 52nd term of an arithmetic sequence, substitute 52 into the given explicit formula and simplify. the answer is 520. Option a is correct.
Step-by-step explanation:
To find the 52nd term of an arithmetic sequence given its explicit formula, you need to substitute the value of n as 52 into the formula. The explicit formula for an arithmetic sequence is a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.
For example, if the explicit formula is a_n = 4 + (n - 1)3, then the 52nd term can be found by substituting 52 for n:
a_52 = 4 + (52 - 1)3 = 4 + 51*3 = 4 + 153 = 520.
Therefore, the answer is 520. Option a is correct.