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What number comes next in the sequence 1, 8, 27, 64 ?
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In this video, we examine the sequence 1, 8, 27, 64, aiming to figure out the next number. We begin by looking for differences between the terms but in this case, we don't find a clear pattern there. Instead, we observe that the numbers themselves reveal a pattern: they are the cubes of integers (n³).
For example, the first term is 1 cubed, which gives us 1. The next term is 2 cubed, which is 2 * 2 * 2, resulting in 8. For the third term, 3 cubed (3 * 3 * 3) gives us 27. For the fourth term, 4 cubed gives us 64. Therefore, we can predict that the next number in the sequence would be 5 cubed. That would give us 125. We can continue the sequence to find all of the additional terms in the sequence.
For example, the first term is 1 cubed, which gives us 1. The next term is 2 cubed, which is 2 * 2 * 2, resulting in 8. For the third term, 3 cubed (3 * 3 * 3) gives us 27. For the fourth term, 4 cubed gives us 64. Therefore, we can predict that the next number in the sequence would be 5 cubed. That would give us 125. We can continue the sequence to find all of the additional terms in the sequence.
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