To find the next three terms of the arithmetic sequence given \(\(-18, -13, -8, -3,\)\), let's follow a step-by-step process:
### Step-by-Step Solution
1. Identify the first term (\(\(a\)\)) and the common difference (\(\(d\)\))
- The first term, denoted \(\(a\)\), is \(\(-18\)\).
- The common difference \(\(d\)\) is calculated by subtracting the first term from the second term:
\(\( d = -13 - (-18) \)\)
\(\[
d = -13 + 18 = 5
\]\)
2. Use the common difference to find the next terms
- The next term in the sequence can be found by adding the common difference to the last known term.
- The last known term provided in the sequence is \(\(-3\)\).
3. Calculate the subsequent terms
\(\[
\text{Next term (5th term)} = -3 + 5 = 2
\]\)
\(\[
\text{Next term (6th term)} = 2 + 5 = 7
\]\)
\(\[
\text{Next term (7th term)} = 7 + 5 = 12
\]\)
Therefore, the next three terms of the sequence following \(\(-3\)\) are \(\(2\)\), \(\(7\)\), and \(\(12\)\).
### Compare with the given options:
- a. -8, -13, -18: This option does not follow the sequence as calculated.
- b. 3, 8, 13: This option does not match our calculated terms.
- c. 2, 7, 12: This option correctly matches our calculated terms.
- d. 0, 5, 10: This option does not match our calculated terms.
### Conclusion
The correct answer is option c. 2, 7, 12.
