Next Number Please! Use inductive reasoning to predict the next number in the list and choose a proper conjecture. 1, 4, 9, 16, 25, 36, 49, ___
Question
Next Number Please! Use inductive reasoning to predict the next number in the list and choose a proper conjecture. 1, 4, 9, 16, 25, 36, 49, ___
Solution
The next number in the sequence is 64. This sequence follows the pattern of perfect squares, where each number is the square of a natural number.
1 = 1^2 4 = 2^2 9 = 3^2 16 = 4^2 25 = 5^2 36 = 6^2 49 = 7^2
So, the next number would be 8^2 = 64.
The conjecture is: "The nth term in the sequence is the square of n."
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