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Consider the sequence: 4, 7, 10, 13, 16, ... Does the formula an 3n+ 4 generate the same sequence? Explain your reasoning. (F.IF.9)

Consider the sequence: 4, 7, 10, 13, 16, ... Does the formula an 3n+ 4 generate the same sequence? Explain your reasoning. (F.IF.9)

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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**Investigating Sequences and Formulas** Consider the sequence: 4, 7, 10, 13, 16, ... Does the formula \(a_n = 3n + 4\) generate the same sequence? Explain your reasoning. (F.IF.9) --- The sequence provided is 4, 7, 10, 13, 16, ... To determine whether the formula \(a_n = 3n + 4\) generates this sequence, we will plug in the values of \(n\) starting from 1 and check if the resulting numbers match the given sequence: - When \(n = 1\): \[ a_1 = 3(1) + 4 = 3 + 4 = 7 \] - When \(n = 2\): \[ a_2 = 3(2) + 4 = 6 + 4 = 10 \] - When \(n = 3\): \[ a_3 = 3(3) + 4 = 9 + 4 = 13 \] - When \(n = 4\): \[ a_4 = 3(4) + 4 = 12 + 4 = 16 \] By evaluating \(a_n\) for the first few terms, we see that this formula does not match the first term of the sequence given, as \(a_1 = 7\) instead of the first term 4. Therefore, the formula \(a_n = 3n + 4\) does **not** generate the same sequence as 4, 7, 10, 13, 16, ... since the first term is different.
Transcribed Image Text:**Investigating Sequences and Formulas** Consider the sequence: 4, 7, 10, 13, 16, ... Does the formula \(a_n = 3n + 4\) generate the same sequence? Explain your reasoning. (F.IF.9) --- The sequence provided is 4, 7, 10, 13, 16, ... To determine whether the formula \(a_n = 3n + 4\) generates this sequence, we will plug in the values of \(n\) starting from 1 and check if the resulting numbers match the given sequence: - When \(n = 1\): \[ a_1 = 3(1) + 4 = 3 + 4 = 7 \] - When \(n = 2\): \[ a_2 = 3(2) + 4 = 6 + 4 = 10 \] - When \(n = 3\): \[ a_3 = 3(3) + 4 = 9 + 4 = 13 \] - When \(n = 4\): \[ a_4 = 3(4) + 4 = 12 + 4 = 16 \] By evaluating \(a_n\) for the first few terms, we see that this formula does not match the first term of the sequence given, as \(a_1 = 7\) instead of the first term 4. Therefore, the formula \(a_n = 3n + 4\) does **not** generate the same sequence as 4, 7, 10, 13, 16, ... since the first term is different.
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