To find an arithmetic sequence of numbers, you can use the following method, which involves defining a first term and a common difference, as explained in the reference:
- Choose a First Term: Begin by selecting any number you want as the initial value in the sequence. According to the reference, "Take any number as the first term."
- Determine a Common Difference: Decide on a number that will be the constant value added to each term to get the next. The reference specifies to "Fix a number as a common difference."
- Generate Subsequent Terms: Add the common difference to the first term to get the second term. Continue adding the common difference to the preceding term to find each successive term. The reference states: "Add the common difference to the first term to obtain the second term," and "To obtain each successive term, keep adding the common difference to its preceding term."
Example:
Let's say we choose 5 as the first term and 3 as the common difference.
- First term: 5
- Second term: 5 + 3 = 8
- Third term: 8 + 3 = 11
- Fourth term: 11 + 3 = 14
- And so on...
Therefore, the sequence would be: 5, 8, 11, 14, ...
In summary, finding an arithmetic sequence involves selecting a starting number and repeatedly adding a fixed value (the common difference) to generate the next number in the sequence.
