1. The problem is to find the next three terms and the rule for the sequence: 1, 4, 9, 16, 25, ... 2. Observe the pattern of the terms: 1 = $1^2$, 4 = $2^2$, 9 = $3^2$, 16 = $4^2$, 25 = $5^2$ 3. This suggests each term is the square of its position in the sequence. 4. Hence, the nth term rule is: $$a_n = n^2$$ 5. The next three terms are found by plugging in $n=6,7,8$: $$a_6 = 6^2 = 36$$ $$a_7 = 7^2 = 49$$ $$a_8 = 8^2 = 64$$ 6. Therefore, the next three terms are 36, 49, and 64.