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What is the fifth term of an arithmetic sequence whose first term is 40 and whose seventh term is 121? A 80 B 94 U 64 D 85

What is the fifth term of an arithmetic sequence whose first term is 40 and whose seventh term is 121? A 80 B 94 U 64 D 85

Algebra and Trigonometry (6th Edition)
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*
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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