{"id":"cb_question_bank:0eeb3559-9c9d-4457-ba3b-f6eda64c52cb","source_id":"cb_question_bank","source_item_id":"0eeb3559-9c9d-4457-ba3b-f6eda64c52cb","external_id":"19eed232-6ab6-4e1d-8586-46e6d6357a09","ibn":null,"question_id":"2c6f214f","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"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 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The first term of a sequence is <math alttext=\"9\"><mn>9</mn>\n</math>. Each term after the first is <math alttext=\"4\"><mn>4</mn>\n</math> times the preceding term. If <math alttext=\"w\"><mi>w</mi>\n</math> represents the <math alttext=\"n\"><mi>n</mi>\n</math>th term of the sequence, which equation gives <math alttext=\"w\"><mi>w</mi>\n</math> in terms of <math alttext=\"n\"><mi>n</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. Since <math alttext=\"w\"><mi>w</mi>\n</math> represents the <math alttext=\"n\"><mi>n</mi>\n</math>th term of the sequence and <math alttext=\"9\"><mn>9</mn>\n</math> is the first term of the sequence, the value of <math alttext=\"w\"><mi>w</mi>\n</math> is <math alttext=\"9\"><mn>9</mn>\n</math> when the value of <math alttext=\"n\"><mi>n</mi>\n</math> is <math alttext=\"1\"><mn>1</mn>\n</math>. Since each term after the first is <math alttext=\"4\"><mn>4</mn>\n</math> times the preceding term, the value of <math alttext=\"w\"><mi>w</mi>\n</math> is&nbsp;<math alttext=\"9 left parenthesis 4 right parenthesis\"><mn>9</mn><mfenced><mn>4</mn></mfenced></math> when the value of <math alttext=\"n\"><mi>n</mi>\n</math> is <math alttext=\"2\"><mn>2</mn>\n</math>. Therefore, the value of <math alttext=\"w\"><mi>w</mi>\n</math> is&nbsp;<math alttext=\"9 left parenthesis 4 right parenthesis left parenthesis 4 right parenthesis\"><mn>9</mn><mfenced><mn>4</mn></mfenced><mfenced><mn>4</mn></mfenced></math>, or&nbsp;<math alttext=\"9 left parenthesis 4 right parenthesis squared\"><mn>9</mn><msup><mfenced><mn>4</mn></mfenced><mn>2</mn></msup></math>, when the value of <math alttext=\"n\"><mi>n</mi>\n</math> is <math alttext=\"3\"><mn>3</mn>\n</math>. More generally, the value of <math alttext=\"w\"><mi>w</mi>\n</math> is&nbsp;<math alttext=\"9 left parenthesis 4 Superscript n minus 1 Baseline right parenthesis\"><mn>9</mn><mfenced><msup><mn>4</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math> for a given value of <math alttext=\"n\"><mi>n</mi>\n</math>. Therefore, the equation&nbsp;<math alttext=\"w equals 9 left parenthesis 4 Superscript n minus 1 Baseline right parenthesis\"><mi>w</mi><mo>=</mo><mn>9</mn><mfenced><msup><mn>4</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math> gives <math alttext=\"w\"><mi>w</mi>\n</math> in terms of <math alttext=\"n\"><mi>n</mi>\n</math>.</p>\n<p>Choice A is incorrect. This equation describes a sequence for which the first term is <math alttext=\"36\"><mn>36</mn>\n</math>, rather than <math alttext=\"9\"><mn>9</mn>\n</math>, and each term after the first is <math alttext=\"9\"><mn>9</mn>\n</math>, rather than <math alttext=\"4\"><mn>4</mn>\n</math>, times the preceding term.&nbsp;</p>\n<p>Choice B is incorrect. This equation describes a sequence for which the first term is <math alttext=\"4\"><mn>4</mn>\n</math>, rather than <math alttext=\"9\"><mn>9</mn>\n</math>, and each term after the first is <math alttext=\"9\"><mn>9</mn>\n</math>, rather than <math alttext=\"4\"><mn>4</mn>\n</math>, times the preceding term.</p>\n<p>Choice C is incorrect. This equation describes a sequence for which the first term is <math alttext=\"36\"><mn>36</mn>\n</math>, rather than <math alttext=\"9\"><mn>9</mn>\n</math>.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.825000+00:00","source_updated_at":"2023-08-02T20:25:59.825000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"w equals 4 left parenthesis 9 Superscript n Baseline right parenthesis\"><mi>w</mi><mo>=</mo><mrow><mn>4</mn></mrow><mfenced><msup><mrow><mn>9</mn></mrow><mi>n</mi></msup></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"w equals 4 left parenthesis 9 Superscript n minus 1 Baseline right parenthesis\"><mi>w</mi><mo>=</mo><mrow><mn>4</mn></mrow><mfenced><msup><mrow><mn>9</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"w equals 9 left parenthesis 4 Superscript n Baseline right parenthesis\"><mi>w</mi><mo>=</mo><mrow><mn>9</mn></mrow><mfenced><msup><mrow><mn>4</mn></mrow><mi>n</mi></msup></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"w equals 9 left parenthesis 4 Superscript n minus 1 Baseline right parenthesis\"><mi>w</mi><mo>=</mo><mrow><mn>9</mn></mrow><mfenced><msup><mrow><mn>4</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}