Final answer:
The 45th term of the arithmetic sequence, which begins with 3 and increases by 6 each time, is found using the formula and results in a value of 267.
Step-by-step explanation:
The sequence provided is an arithmetic sequence where each term increases by 6. To find the 45th term, we use the arithmetic sequence formula Tn = a + (n-1)d, where Tn is the nth term, a is the first term, n is the term number, and d is the common difference.
Here, the first term a = 3, and the common difference d = 6. Plugging the values into the formula gives us:
T45 = 3 + (45-1)×6
T45 = 3 + 44×6
T45 = 3 + 264
T45 = 267
Therefore, the 45th term of the sequence is 267.