{"@context":"https://schema.org/","@type":"Quiz","name":"

The first term of a sequence is 9. Each term after the first is 4 times the preceding term. If $w$ represents the $n$th term of the sequence, which equation gives $w$ in terms of $n$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-9"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

The first term of a sequence is 9. Each term after the first is 4 times the preceding term. If $w$ represents the $n$th term of the sequence, which equation gives $w$ in terms of $n$?

","comment":{"@type":"Comment","text":"

Choice D is correct. Since $w$ represents the $n$th term of the sequence and $9$ is the first term of the sequence, the value of $w$ is $9$ when the value of $n$ is $1$ . Since each term after the first is $4$ times the preceding term, the value of $w$ is $9(4)$ when the value of $n$ is $2$. Therefore, the value of $w$ is $9(4)(4)$, or $9(4)^{2}$, when the value of $n$ is $3$. More generally, the value of $w$ is $9(4^{n-1})$ for a given value of $n$. Therefore, the equation $w=9(4^{n-1})$ gives $w$ in terms of $n$.

Choice A is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term.

Choice B is incorrect. This equation describes a sequence for which the first term is $4$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term.

Choice C is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$.

"},"encodingFormat":"text/markdown","text":"

The first term of a sequence is 9. Each term after the first is 4 times the preceding term. If $w$ represents the $n$th term of the sequence, which equation gives $w$ in terms of $n$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$w=4(9^{n})$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$w=4(9^{n-1})$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$w=9(4^{n})$

"}],"acceptedAnswer":{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$w=9(4^{n-1})$

","comment":{"@type":"Comment","text":"

Choice A is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term.

Choice B is incorrect. This equation describes a sequence for which the first term is $4$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term.

Choice C is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$.

"},"answerExplanation":{"@type":"Comment","text":"

Choice A is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term.

Choice B is incorrect. This equation describes a sequence for which the first term is $4$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term.

Choice C is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-9"}