1. **State the problem:** We are given the sequence 16, 36, 64, 81, 100 and asked to find the next two terms. 2. **Analyze the sequence:** Let's look for a pattern. Notice that these numbers are perfect squares: $$16 = 4^2$$ $$36 = 6^2$$ $$64 = 8^2$$ $$81 = 9^2$$ $$100 = 10^2$$ 3. **Identify the pattern in the bases:** The bases are 4, 6, 8, 9, 10. They don't increase by a constant difference, so let's check if there's another pattern. 4. **Check the sequence of bases:** 4, 6, 8, 9, 10 - From 4 to 6: +2 - From 6 to 8: +2 - From 8 to 9: +1 - From 9 to 10: +1 5. **Predict the next bases:** Following the pattern of increments (+2, +2, +1, +1), the next increments might be +2, +2 again. 6. **Calculate the next bases:** - Next base after 10: 10 + 2 = 12 - Next base after 12: 12 + 2 = 14 7. **Calculate the next terms:** $$12^2 = 144$$ $$14^2 = 196$$ **Final answer:** The next two terms in the sequence are 144 and 196.