{"id":"act_quizme:math:q3:05","source_id":"act_quizme","source_item_id":"math-q3-05","external_id":"87f10a0bd43cf841","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":5,"scored":true,"layout_warning":null,"stem":"The first 5 terms of an arithmetic sequence are 7, 21, 35, 49, and 63. Let t subscript n t n represent the nth n th term of the sequence. What is the value of t subscript 25 t 25 ?","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"><div class=\"item-content\" id=\"p50\"> \t\t\t\t\t \t\t\t\t\t<p>The first 5 terms of an arithmetic sequence are 7, 21, 35, 49, and 63. Let&nbsp;<span class=\"visually-hidden\">t subscript n</span><math class=\"srTransform\"><msub><mi>t</mi><mi>n</mi></msub></math>&nbsp;represent the <span style=\"white-space: nowrap;\"><span class=\"visually-hidden\"></span><span class=\"visuallyhidden\">nth</span><span><math><mi>n</mi></math>th</span></span> term of the sequence. What is the value of <span style=\"white-space: nowrap;\"><span class=\"visually-hidden\">t subscript 25</span><math class=\"srTransform\"><msub><mi>t</mi><mn>25</mn></msub></math>?</span></p>  \t\t\t\t</div> \t\t\t\t</div>\n<div><div class=\"math-answer-select-wrap\"></div></div>","rationale_html":"<p><strong>A.</strong> <strong>Incorrect.</strong> Remember that the <span style=\"white-space: nowrap;\"><math><mi>n</mi></math>th</span> term of an arithmetic sequence, <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mi>n</mi></msub></math>,</span> can be calculated using the formula&nbsp;<math><msub><mi>t</mi><mi>n</mi></msub><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mi>d</mi></math>&nbsp;where n is the number of terms, d is the common difference, and&nbsp;<math><msub><mi>t</mi><mn>1</mn></msub></math>&nbsp;is the first term. You may have calculated <span style=\"white-space: nowrap;\"><math><mn>25</mn><mo>×</mo><mn>7</mn></math>.</span><span style=\"white-space: nowrap;\">&nbsp;</span></p><p><strong>B.</strong> <strong>Correct.</strong> Remember that the <span style=\"white-space: nowrap;\"><math><mi>n</mi></math>th</span> term of an arithmetic sequence, <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mi>n</mi></msub></math>,</span> can be calculated using the formula&nbsp;<math><msub><mi>t</mi><mi>n</mi></msub><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mi>d</mi></math>&nbsp;where n is the number of terms, d is the common difference, and&nbsp;<math><msub><mi>t</mi><mn>1</mn></msub></math>&nbsp;is the first term. Here, <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mn>7</mn></math>,</span> <span style=\"white-space: nowrap;\"><math><mi>n</mi><mo>=</mo><mn>25</mn></math>,</span> and the common difference can be found by subtracting any 2 consecutive terms, <span style=\"white-space: nowrap;\"><math><mi>d</mi><mo>=</mo><mn>21</mn><mo>-</mo><mn>7</mn><mo>=</mo><mn>14</mn></math>.</span> Substituting these values, <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mn>25</mn></msub><mo>=</mo><mn>7</mn><mo>+</mo><mfenced><mrow><mn>25</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mn>14</mn><mo>=</mo><mn>7</mn><mo>+</mo><mn>336</mn><mo>=</mo><mn>343</mn></math>.</span></p><p><strong>C.</strong> <strong>Incorrect.</strong> Remember that the <span style=\"white-space: nowrap;\"><math><mi>n</mi></math>th</span> term of an arithmetic sequence, <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mi>n</mi></msub></math>,</span> can be calculated using the formula&nbsp;<math><msub><mi>t</mi><mi>n</mi></msub><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mi>d</mi></math>&nbsp;where n is the number of terms, d is the common difference, and&nbsp;<math><msub><mi>t</mi><mn>1</mn></msub></math>&nbsp;is the first term. You may have calculated <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mi>n</mi></msub><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><mi>n</mi><mi>d</mi></math>.</span></p><p><strong>D.</strong> <strong>Incorrect.</strong> Remember that the <span style=\"white-space: nowrap;\"><math><mi>n</mi></math>th</span> term of an arithmetic sequence, <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mi>n</mi></msub></math>,</span> can be calculated using the formula&nbsp;<math><msub><mi>t</mi><mi>n</mi></msub><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mi>d</mi></math>&nbsp;where n is the number of terms, d is the common difference, and&nbsp;<math><msub><mi>t</mi><mn>1</mn></msub></math>&nbsp;is the first term. You may have calculated <span style=\"white-space: nowrap;\"><math><msub><mi>t</mi><mi>n</mi></msub><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mi>d</mi></math>.</span></p>","correct_answer":["B"],"equiv_key":"e81a1e5c0fabf2d3f7c44460","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>175</p>","ord":0},{"label":"B","content_html":"<p>343</p>","ord":1},{"label":"C","content_html":"<p>357</p>","ord":2},{"label":"D","content_html":"<p>371</p>","ord":3}],"passage":null,"attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. 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