Write the arithmetic sequence – 14, – 17, – 20, – 23, ... in the standard form: An

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Write the arithmetic sequence −14, −17, −20, −23, … in the standard form:**

\( a_n = \) \_\_\_\_\_\_\_ .

**Explanation:**

This task involves expressing an arithmetic sequence in its standard formula form. The sequence provided is −14, −17, −20, −23, and continues indefinitely.

To find the standard form \( a_n = a_1 + (n-1)d \):

- \( a_1 \) is the first term of the sequence, which is −14.
- \( d \) is the common difference between terms, which can be calculated as the difference between any two consecutive terms. Here, \( d = -17 - (-14) = -3 \).

By substituting these values into the formula, the standard form of the sequence can be calculated.
Transcribed Image Text:**Write the arithmetic sequence −14, −17, −20, −23, … in the standard form:** \( a_n = \) \_\_\_\_\_\_\_ . **Explanation:** This task involves expressing an arithmetic sequence in its standard formula form. The sequence provided is −14, −17, −20, −23, and continues indefinitely. To find the standard form \( a_n = a_1 + (n-1)d \): - \( a_1 \) is the first term of the sequence, which is −14. - \( d \) is the common difference between terms, which can be calculated as the difference between any two consecutive terms. Here, \( d = -17 - (-14) = -3 \). By substituting these values into the formula, the standard form of the sequence can be calculated.
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