Answer: A) If the sequence starts with the terms 3 and 12, and it is arithmetic, we can determine the common difference between terms to find the next two terms.
Explanation:
To find the common difference, we subtract the second term from the first term:
12 - 3 = 9
The common difference in this case is 9.
To find the next term, we add the common difference to the last term:
12 + 9 = 21
Therefore, the next term in the arithmetic sequence is 21.
To find the term after that, we again add the common difference:
21 + 9 = 30
Therefore, the term after 21 in the arithmetic sequence is 30.
B) If the sequence starts with the terms 3 and 12, and it is geometric, we can determine the common ratio between terms to find the next two terms.
To find the common ratio, we divide the second term by the first term:
12 ÷ 3 = 4
The common ratio in this case is 4.
To find the next term, we multiply the last term by the common ratio:
12 × 4 = 48
Therefore, the next term in the geometric sequence is 48.
To find the term after that, we again multiply the last term by the common ratio:
48 × 4 = 192
Therefore, the term after 48 in the geometric sequence is 192.
C) If the sequence is neither arithmetic nor geometric, there is no specific pattern or rule to determine the next terms. Without additional information, we cannot provide a definitive answer for the next two terms in this case. The sequence could follow a different pattern or have no identifiable pattern at all.