Final answer:
The nth term of the arithmetic sequence 3, 12, 21, 30, 39 is 9n - 6, derived using the formula for the nth term of an arithmetic sequence.
Step-by-step explanation:
The sequence given is 3, 12, 21, 30, 39. This is an arithmetic sequence, where each term increases by a common difference. To find the nth term of an arithmetic sequence, you use the formula tn = a + (n-1)d, where a is the first term and d is the common difference. In this sequence, the first term a is 3, and the common difference d is 9 (because 12 - 3 = 9). Plugging these values into the formula gives us the nth term: tn = 3 + (n-1)9 = 3 + 9n - 9 = 9n - 6. Therefore, the nth term of the sequence is 9n - 6.
The given sequence is 3, 12, 21, 30, 39. To find the nth term of this sequence, we need to analyze the pattern. If we look closely, we can see that each term is obtained by adding a multiple of 9 to the previous term. Specifically, the first term (3) is obtained by adding 9*0 to 3, the second term (12) is obtained by adding 9*1 to 3, the third term (21) is obtained by adding 9*2 to 3, and so on. So, the nth term can be obtained by adding 9*(n-1) to 3.