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The non-recursively defined formula for writing an arithmetic sequence is given by: an = C+ (n - 1)d, n 2 1. O True O False

The non-recursively defined formula for writing an arithmetic sequence is given by: an = C+ (n - 1)d, n 2 1. O True O False

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Question:** The non-recursively defined formula for writing an arithmetic sequence is given by: \( a_n = c + (n - 1)d \), \( n \geq 1 \). - O True - O False **Explanation for Educational Website:** This question tests the understanding of arithmetic sequences. The formula \( a_n = c + (n - 1)d \) is indeed the non-recursive (or explicit) formula for an arithmetic sequence, where: - \( a_n \) is the nth term of the sequence. - \( c \) is the first term of the sequence. - \( d \) is the common difference between consecutive terms. - \( n \) is the term number, starting at 1. Understanding this formula allows you to compute any term in the sequence without knowing the previous term, providing a direct calculation method.
Transcribed Image Text:**Question:** The non-recursively defined formula for writing an arithmetic sequence is given by: \( a_n = c + (n - 1)d \), \( n \geq 1 \). - O True - O False **Explanation for Educational Website:** This question tests the understanding of arithmetic sequences. The formula \( a_n = c + (n - 1)d \) is indeed the non-recursive (or explicit) formula for an arithmetic sequence, where: - \( a_n \) is the nth term of the sequence. - \( c \) is the first term of the sequence. - \( d \) is the common difference between consecutive terms. - \( n \) is the term number, starting at 1. Understanding this formula allows you to compute any term in the sequence without knowing the previous term, providing a direct calculation method.
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