Subjects algebra

Cubic Sequence 67E946

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Question: g. 1; 8; 27; 64; ...
1. **State the problem:** We are given the sequence $1, 8, 27, 64, \ldots$ and asked to describe the pattern. 2. **Identify the pattern:** Notice that each term looks like a cube of an integer: $$1 = 1^3$$ $$8 = 2^3$$ $$27 = 3^3$$ $$64 = 4^3$$ 3. **General formula:** The $n$-th term of the sequence can be expressed as: $$a_n = n^3$$ 4. **Explanation:** This means the sequence consists of perfect cubes of consecutive natural numbers starting from 1. 5. **Next term:** The next term after $64$ (which is $4^3$) is: $$5^3 = 125$$ **Final answer:** The sequence is the cubes of natural numbers: $1^3, 2^3, 3^3, 4^3, \ldots$