Pregunta
The following sequence is a combination of
arithmetic and geometric sequence:
arithmetic and geometric sequence:
Ask by Marshall Rowe. in South Africa
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The next two terms are 21 and 24. The difference between the 20th and 21st terms is 1473.
Solución
Let’s analyze the given sequence and solve the problems step by step.
Given Sequence:
The sequence alternates between two different patterns:
- Odd-positioned terms (1st, 3rd, 5th, …): These terms form an arithmetic sequence.
- Even-positioned terms (2nd, 4th, 6th, …): These terms form a geometric sequence.
4.1.1 Write Down the Next Two Terms
1. Identify the Patterns:
-
Odd Positions (Arithmetic Sequence):
- Terms: 3, 9, 15, …
- Common Difference (d):
- General Formula:
where is the position in the odd sequence.
-
Even Positions (Geometric Sequence):
- Terms: 3, 6, 12, …
- Common Ratio ®:
- General Formula:
where is the position in the even sequence.
2. Determine the Next Two Terms:
-
7th Term (Odd Position):
-
8th Term (Even Position):
**Answer: The next two terms are 21 and 24.
4.1.2 Determine
1. Find
-
20th Term (
) is an even-positioned term: -
21st Term (
) is an odd-positioned term:
2. Calculate the Difference:
**Answer:
Summary:
- Next Two Terms: 21 and 24
- Difference
: 1473
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Simplifique esta solución Mind Expander
To determine the next two terms in the sequence, let’s break it down. The alternating pattern suggests that every other term forms an arithmetic sequence, while the others form a geometric one.
The arithmetic sequence can be observed as:
3, 6, 9, 12 (which increases by 3). So the next term is 15.
The geometric sequence is:
3, 9, 15 (which appears to multiply by 3, and then increases by 6). Continuing this pattern, the next term becomes
Thus, we predict the next two terms are 15 and 18 for the arithmetic and 22.5 and 27 for the geometric.
3, 6, 9, 12 (which increases by 3). So the next term is 15.
The geometric sequence is:
3, 9, 15 (which appears to multiply by 3, and then increases by 6). Continuing this pattern, the next term becomes
Thus, we predict the next two terms are 15 and 18 for the arithmetic and 22.5 and 27 for the geometric.
Now, moving on to
To find these terms, we note the pattern continues:
The 20th arithmetic term is 3 + (19 × 3) = 60, and the 21st term follows the sequence down to 18 and assumed terminal growth, leading to
To find these terms, we note the pattern continues:
The 20th arithmetic term is 3 + (19 × 3) = 60, and the 21st term follows the sequence down to 18 and assumed terminal growth, leading to
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