Find the 53rd term of the arithmetic sequence –12, -1, 10, ...

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:**

Find the 53rd term of the arithmetic sequence \( -12, -1, 10, \ldots \).

**Answer Submission Form:**

Below the problem statement, there is an answer submission form where students can input their answers. The form includes:
- A text box labeled "Answer:" where students can enter their solution.
- A "Submit Answer" button to send their response.

**Explanation:**

To find the 53rd term of an arithmetic sequence, use the formula for the nth term of an arithmetic sequence:

\[ a_n = a_1 + (n-1) \cdot d \]

Here:
- \( a_n \) is the nth term.
- \( a_1 \) is the first term.
- \( n \) is the term number.
- \( d \) is the common difference.

For the given sequence \( -12, -1, 10, \ldots \):
- The first term \( a_1 = -12 \).
- The common difference \( d = -1 - (-12) = 11 \).

Now, plug in the values:

\[ a_{53} = -12 + (53-1) \cdot 11 \]
\[ a_{53} = -12 + 52 \cdot 11 \]
\[ a_{53} = -12 + 572 \]
\[ a_{53} = 560 \]

Therefore, the 53rd term of the arithmetic sequence is 560.
Transcribed Image Text:**Problem Statement:** Find the 53rd term of the arithmetic sequence \( -12, -1, 10, \ldots \). **Answer Submission Form:** Below the problem statement, there is an answer submission form where students can input their answers. The form includes: - A text box labeled "Answer:" where students can enter their solution. - A "Submit Answer" button to send their response. **Explanation:** To find the 53rd term of an arithmetic sequence, use the formula for the nth term of an arithmetic sequence: \[ a_n = a_1 + (n-1) \cdot d \] Here: - \( a_n \) is the nth term. - \( a_1 \) is the first term. - \( n \) is the term number. - \( d \) is the common difference. For the given sequence \( -12, -1, 10, \ldots \): - The first term \( a_1 = -12 \). - The common difference \( d = -1 - (-12) = 11 \). Now, plug in the values: \[ a_{53} = -12 + (53-1) \cdot 11 \] \[ a_{53} = -12 + 52 \cdot 11 \] \[ a_{53} = -12 + 572 \] \[ a_{53} = 560 \] Therefore, the 53rd term of the arithmetic sequence is 560.
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