Final answer:
There are 6 different arithmetic sequences that can be created with a first term of 1, a last term of 19, and a positive integer common difference.
Step-by-step explanation:
To determine the number of different arithmetic sequences that can be created with a first term of 1, a last term of 19, and a positive integer common difference, we need to find the number of positive divisors of the difference between the last term and the first term.
The difference between the last term and the first term is 19 - 1 = 18. The positive divisors of 18 are 1, 2, 3, 6, 9, and 18, so there are 6 different positive divisors. Therefore, there are 6 different arithmetic sequences that can be created.