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To find the general rule for the sequence 10, 15, 20:
1. Identify the pattern:
- The difference between terms is constant at 5.
2. General rule for an arithmetic sequence:
- The formula is: an = a1 + (n - 1) * d
Where:
- a_n = the nth term
- a_1 = the first term
- d = common difference
- n = position of the term
3. Apply to the given sequence:
- First term (a_1) = 10
- Common difference (d) = 5
General rule:
an = 10 + (n - 1) * 5
- Simplify: