Use the arithmetic sequence an = 6 + (n - 1)4 to find the following. a) The first five terms are: ,and b) The common difference is d =
Use the arithmetic sequence an = 6 + (n - 1)4 to find the following. a) The first five terms are: ,and b) The common difference is d =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Arithmetic Sequence Exploration**
In this activity, we're using the arithmetic sequence formula \( a_n = 6 + (n-1)4 \) to find specified elements of the sequence.
**Tasks:**
a) **Identify the First Five Terms:**
- Calculate and list the first five terms of the sequence in the provided spaces.
b) **Determine the Common Difference:**
- Find and enter the common difference \( d \) of the sequence.
**Guidance:**
- The formula represents a linear sequence where \( a_n \) is the nth term, 6 is the first term, and the expression \((n-1)4\) indicates the increment between consecutive terms.
- Recall the common difference \( d \) is the constant increment between each term in the sequence.
Use this exercise to enhance your understanding of pattern recognition and algebraic expressions in arithmetic sequences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9134c255-a2be-4530-8da1-a6d66778d97d%2F96de7940-b70b-4d48-9189-a948628bc512%2F4ptx7ds_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Arithmetic Sequence Exploration**
In this activity, we're using the arithmetic sequence formula \( a_n = 6 + (n-1)4 \) to find specified elements of the sequence.
**Tasks:**
a) **Identify the First Five Terms:**
- Calculate and list the first five terms of the sequence in the provided spaces.
b) **Determine the Common Difference:**
- Find and enter the common difference \( d \) of the sequence.
**Guidance:**
- The formula represents a linear sequence where \( a_n \) is the nth term, 6 is the first term, and the expression \((n-1)4\) indicates the increment between consecutive terms.
- Recall the common difference \( d \) is the constant increment between each term in the sequence.
Use this exercise to enhance your understanding of pattern recognition and algebraic expressions in arithmetic sequences.
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