find the common difference in the arithmetic sequence 1, 3/2, 2, 5/2, 3, ...
Answer (1)
Answer:The common difference in the arithmetic sequence 1, 3/2, 2, 5/2, 3,… is 1/2.Step-by-step explanation:To find the common difference in the arithmetic sequence 1, 3/2, 2, 5/2, 3,…, we need to identify the pattern between consecutive terms.Step 1: Identify the patternWe can see that each term is increasing by a certain amount. For example, the difference between the first and second term is 3/2 - 1 = 1/2. Similarly, the difference between the second and third term is 2 - 3/2 = 1/2. This suggests that the common difference between consecutive terms is 1/2.Step 2: Calculate the common differenceTo confirm our observation, we can calculate the common difference using the formula for the nth term of an arithmetic sequence: a + (n-1)d, where a is the first term, n is the term number, and d is the common difference.For the first term (a = 1), the second term (n = 2) is 1 + (2-1)(1/2) = 1 + 1/2 = 3/2. This confirms that the common difference is indeed 1/2.Answer: The common difference in the arithmetic sequence 1, 3/2, 2, 5/2, 3,… is 1/2.
