1. Let's analyze each sequence to find the rule. 2. Sequence 1: 5, 10, 14, 16, 18 - Differences: 10-5=5, 14-10=4, 16-14=2, 18-16=2 - The differences are not consistent, but seem to decrease and then stabilize. - Possibly the rule is adding decreasing increments: +5, +4, +2, +2. 3. Sequence 2: 3, 8, 13, 45, 55, 6 - Differences: 8-3=5, 13-8=5, 45-13=32, 55-45=10, 6-55=-49 - The differences vary widely, no clear arithmetic progression. - Possibly a mixed or non-linear rule. 4. Sequence 3: 4, 12, 30, 40, 50, 60 - Differences: 12-4=8, 30-12=18, 40-30=10, 50-40=10, 60-50=10 - After initial irregular differences, the sequence increases by 10 consistently. 5. Summary: - Sequence 1 rule: add 5, then 4, then 2 repeatedly. - Sequence 2 rule: no clear arithmetic pattern; possibly irregular or complex. - Sequence 3 rule: after initial steps, add 10 each time. Final answers: - Sequence 1 rule: add 5, then 4, then 2, then 2. - Sequence 2 rule: no simple arithmetic rule. - Sequence 3 rule: add 8, then 18, then 10 repeatedly.