Final answer:
The nth term of the arithmetic sequence with a first term of 5 and a pattern of adding 3 to the previous term is given by the equation f(n) = 3n + 2.
Step-by-step explanation:
The question seeks to find an equation for the nth term of a sequence given its first term and the pattern it follows. Since the first term, f(1), is given as 5 and the subsequent terms can be found by adding 3 to the previous term (f(n) = f(n-1) + 3), we can deduce that this is an arithmetic sequence. To find the nth term, we use the formula for an arithmetic sequence, which is: an = a1 + (n - 1)d, where a1 is the first term and d is the common difference. Here, a1 would be 5, and the common difference, d, would be 3.
The equation for the nth term thus becomes f(n) = 5 + (n - 1) × 3, which simplifies to f(n) = 3n + 2.