Sumali sa komunidad ng IDNStudy.com at simulang makuha ang mga sagot na kailangan mo. Makakuha ng mga kumpletong sagot sa lahat ng iyong mga tanong mula sa aming network ng mga eksperto.
Answer:
An arithmetic sequence has a constant difference between consecutive terms. Let's check for a common difference:
[tex]8 - 1 = 7[/tex]
[tex]27 - 8 = 19[/tex]
Since the differences are not equal, (1, 8, 27) is not an arithmetic sequence.
A geometric sequence has a constant ratio between consecutive terms. Let's check for a common ratio:
[tex]\frac{8}{1} = 8[/tex]
[tex]\frac{27}{8} \approx 3.375[/tex]
Since the ratios are not equal, (1, 8, 27) is not a geometric sequence.
Other Type: Polynomial Sequence
This sequence can be identified as a sequence of cubes. Let's analyze the terms:
[tex]1 = 1^3[/tex]
[tex]8 = 2^3[/tex]
[tex]27 = 3^3[/tex]
The given sequence (1, 8, 27) is the sequence of the cubes of the first three positive integers:
[tex]n^3 \text{ where } n = 1, 2, 3, \ldots[/tex]
Therefore, the next term in this sequence (for ( n = 4 )) would be:
[tex]4^3 = 64[/tex]
- Arithmetic Sequence: No, because it does not have a constant difference.
- Geometric Sequence: No, because it does not have a constant ratio.
- Polynomial Sequence (Cubic): Yes, the sequence represents the cubes of natural numbers ( n³ ).
Thus, the sequence (1, 8, 27) is best described as a sequence of cubes.