1. The problem gives the sequence: 1, 8, 27, 64, 125, ... 2. Identify the pattern: these are cubes of natural numbers. 3. Check each term: - $1 = 1^3$ - $8 = 2^3$ - $27 = 3^3$ - $64 = 4^3$ - $125 = 5^3$ 4. Thus, the $n$th term of the sequence is given by the rule $a_n = n^3$. 5. Find the next three terms by substituting $n=6, 7, 8$: - $a_6 = 6^3 = 216$ - $a_7 = 7^3 = 343$ - $a_8 = 8^3 = 512$ 6. Therefore, the next three terms are 216, 343, and 512. 7. Final answer: - Next three terms: 216, 343, 512 - Rule: $a_n = n^3$