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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![**Question 2**
What is the fifth term of an arithmetic sequence whose first term is 40 and whose seventh term is 121?
A) 80
B) 94
C) 64
D) 85
*To solve this problem, determine the common difference \(d\) using the formula for the \(n\)th term of an arithmetic sequence:*
\[a_n = a_1 + (n-1) \times d\]
*Given:*
First term, \(a_1 = 40\)
Seventh term, \(a_7 = 121\)
*Substitute to find \(d\):*
\[121 = 40 + (7-1) \times d\]
\[121 = 40 + 6d\]
\[81 = 6d\]
\[d = \frac{81}{6} = 13.5\]
*Find the fifth term, \(a_5\):*
\[a_5 = 40 + (5-1) \times 13.5\]
\[a_5 = 40 + 4 \times 13.5\]
\[a_5 = 40 + 54\]
\[a_5 = 94\]
*Correct Answer: B) 94*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82a839f4-6217-4972-8779-40aed17e5667%2Ff21dd561-d7cc-4671-9a39-9be2d7dded85%2Fmoogtgg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 2**
What is the fifth term of an arithmetic sequence whose first term is 40 and whose seventh term is 121?
A) 80
B) 94
C) 64
D) 85
*To solve this problem, determine the common difference \(d\) using the formula for the \(n\)th term of an arithmetic sequence:*
\[a_n = a_1 + (n-1) \times d\]
*Given:*
First term, \(a_1 = 40\)
Seventh term, \(a_7 = 121\)
*Substitute to find \(d\):*
\[121 = 40 + (7-1) \times d\]
\[121 = 40 + 6d\]
\[81 = 6d\]
\[d = \frac{81}{6} = 13.5\]
*Find the fifth term, \(a_5\):*
\[a_5 = 40 + (5-1) \times 13.5\]
\[a_5 = 40 + 4 \times 13.5\]
\[a_5 = 40 + 54\]
\[a_5 = 94\]
*Correct Answer: B) 94*
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