Tell whether the sequence is arithmetic. If it is, what is the common difference?
What is the sequence?
To determine if a sequence is arithmetic, you need to check if there is a constant difference between each consecutive term.
Here are the steps to determine whether a sequence is arithmetic and find the common difference:
1. Write down the terms of the sequence. Let's say the sequence is {a, b, c, d, e, f, ...}.
2. Calculate the differences between consecutive terms:
- Subtract the second term from the first term: b - a.
- Subtract the third term from the second term: c - b.
- Continue this process until you compute the difference between the last two terms: (f - e).
3. Compare all the differences you calculated in step 2. If all the differences are equal, then the sequence is arithmetic.
4. To find the common difference, you can choose any pair of consecutive terms and subtract the first term from the second term. This will give you the value of the common difference between each term in the sequence.
If all the differences between consecutive terms are equal, then the sequence is arithmetic, and the common difference is the value obtained in step 4. If the differences are not equal, then the sequence is not arithmetic.