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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**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.
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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