What is the common difference of an arithmetic sequence that starts with 3 and has subsequent terms of 5, 7, 9? (A) 3 (B) 6 (C) 1 (D) 2
Answer (1)
To find the common difference of an arithmetic sequence, we start by identifying the pattern between consecutive terms. An arithmetic sequence is defined by a sequence of numbers in which the difference of any two successive members is a constant, called the common difference.
Let's analyze the given sequence:
The sequence starts at 3.
The next term is 5.
Then, the next term is 7.
The following term is 9.
We need to find the difference between successive terms to determine the common difference.
The difference between the second term (5) and the first term (3) is calculated as follows: 5 − 3 = 2
The difference between the third term (7) and the second term (5) is: 7 − 5 = 2
The difference between the fourth term (9) and the third term (7) is: 9 − 7 = 2
Since the difference is consistent across all pairs of consecutive terms, the common difference for this arithmetic sequence is 2.
So, the answer to the question is (D) 2.
