Final answer:
After calculating the first five terms of the sequence: 1/3, 1/5, 1/7, 1/9, 1/11, it's clear that the differences between terms are not constant, hence the sequence is not arithmetic and does not have a common difference.
Step-by-step explanation:
To find the first five terms of the sequence and determine if it is arithmetic, we begin by substituting the respective values of n into the given formula: an = 1 / (1 + 2n).
- For n = 1, a1 = 1 / (1 + 2*1) = 1/3.
- For n = 2, a2 = 1 / (1 + 2*2) = 1/5.
- For n = 3, a3 = 1 / (1 + 2*3) = 1/7.
- For n = 4, a4 = 1 / (1 + 2*4) = 1/9.
- For n = 5, a5 = 1 / (1 + 2*5) = 1/11.
By examining these terms, we can see that the sequence is not arithmetic since the difference between successive terms is not constant. In an arithmetic sequence, the difference (known as the common difference) must be the same for each pair of consecutive terms. Here, the differences are 1/5 - 1/3 = -2/15, 1/7 - 1/5 = -2/35, 1/9 - 1/7 = -2/63, etc., which are not the same. Therefore, the given sequence is not arithmetic, and it does not have a common difference.