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4297c1b8-5fa5-4027-8686-b300337348aa.html
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<!--Do not edit this div tag. It must surround the interaction block-->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="4cbb9077-36a0-41da-a973-346270ec3474" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="4346f584-c163-4d4f-af5b-ff3f4e32e6dc" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(c(n)=c(n-1)+6\)" data-solution-options='["\\(a(n)=7\\cdot a(n-1)\\)", "\\(b(n)=\\frac12b(n-1)\\)", "\\(c(n)=c(n-1)+6\\)", "\\(d(n)=d(n-1)+20\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For #1–3, match each sequence with one of the definitions. Note that only the part of the definition showing the relationship between the current term and the previous term is given so as not to give away the solutions.</p>
<ol class="os-raise-noindent" type="1">
<li>6, 12, 18, 24</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(c(n)=c(n-1)+6\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 4.17.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(c(n)=c(n−1)+6\). </p>
</div>
</div>
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="f0bb4279-bc18-410e-9f1e-cf2a4f7c4a18" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(a{(\mathrm n})=7\cdot a(n-1)\)" data-solution-options='["\\(a{(\\mathrm n})=7\\cdot a(n-1)\\)", "\\(b(n)=\\frac12b(n-1)\\)", "\\(c(n)=c(n-1)+6\\)", "\\(d(n)=d(n-1)+20\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="1">
<li>2, 14, 98, 686</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(a(n)=7\cdot a(n-1)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.17.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(a(n))=7\cdot a(n-1)\). </p>
</div>
</div>
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="9e8f3213-c781-466f-b0c9-960969c82d9e" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(b(n)=\frac12b(n-1)\)" data-solution-options='["\\(a{(\\mathrm n})=7\\cdot a(n-1)\\)", "\\(b(n)=\\frac12b(n-1)\\)", "\\(c(n)=c(n-1)+6\\)", "\\(d(n)=d(n-1)+20\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="1">
<li>160, 80, 40, 20</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(b(n)=\frac{1}{2}b(n-1)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 4.17.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(b(n)=\frac12b(n-1)\). </p>
</div>
</div>
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="3a1ca587-2e2c-4c2b-9366-97eff10d778b" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="7, 4, 1, -2, -5, arithmetic" data-solution-options='["7, 4, 1, -2, -5, geometric", "7, -21, 63, -189, geometric", "7, -21, 63, -189, arithmetic", "7, 4, 1, -2, -5, arithmetic"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For #4–5, select the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.</p>
<ol class="os-raise-noindent" start="4" type="1">
<li>\(a(1)=7\), \(a(n)=a(n−1)−3\) for \(n≥2\).</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 7, 4, 1, –2, –5, arithmetic</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.17.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 7, 4, 1, –2, –5, arithmetic. </p>
</div>
</div>
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="a3ae435e-517b-4dd8-a419-01290f5af8d7" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="3, 30, 300, 3000, 30000, geometric" data-solution-options='["3, 30, 300, 3000, 30000, arithmetic", "3, 30, 300, 3000, 30000, geometric", "3, 13, 23, 33, 43, geometric", "3, 13, 23, 33, 43, arithmetic"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="1">
<li>\(c(1)=3\), \(c(n)=10⋅c(n−1)\) for \(n≥2\).</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 3, 30, 300, 3000, 30000, geometric</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 4.17.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 3, 30, 300, 3000, 30000, geometric. </p>
</div>
</div>
<!--Q6-->
<div class="os-raise-ib-pset-problem" data-content-id="50bf737d-9ce3-4460-aee2-daf2767eecf9" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(c(n)=5 \cdot c(n-1)\)" data-solution-options='["\\(a(n)=\\frac{1}{3} \\cdot a(n-1)\\)", "\\(b(n)=b(n-1)-4\\)", "\\(c(n)=5 \\cdot c(n-1)\\)", "\\(d(n)=d(n-1)+n-1\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For #6–9, match each sequence with one of the recursive definitions. Note that only the part of the definition showing the relationship between the current term and the previous term is given so as not to give away the solutions.</p>
<ol class="os-raise-noindent" start="6" type="1">
<li>3, 15, 75, 375</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(c(n)=5 \cdot c(n-1)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.17.2–4.17.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(c(n)=5\cdot c(n−1)\). </p>
</div>
</div>
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="de90b110-dd9b-4dab-a220-43138f2ab7ac" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(a(n)=\frac{1}{3}\cdot a(n-1)\)" data-solution-options='["\\(a(n)=\\frac{1}{3}\\cdot a(n-1)\\)", "\\(b(n)=b(n-1)-4\\)", "\\(c(n)=5 \\cdot c(n-1)\\)", "\\(d(n)=d(n-1)+n-1\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" type="1">
<li>18, 6, 2, \(\frac{2}{3}\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(a(n)=\frac{1}{3}a(n-1)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.17.2–4.17.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(a(n)=\frac{1}{3}\cdot a(n-1)\). </p>
</div>
</div>
<!--Q9-->
<div class="os-raise-ib-pset-problem" data-content-id="cbd7a717-07d5-4ad6-a639-e457a6d9956c" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(b(n)=b(n-1)-4\)" data-solution-options='["\\(a(n)=\\frac{1}{3}\\cdot a(n-1)\\)", "\\(b(n)=b(n-1)-4\\)", "\\(c(n)=5 \\cdot c(n-1)\\)", "\\(d(n)=d(n-1)+n-1\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8" type="1">
<li>17, 13, 9, 5</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(b(n)=b(n-1)-4\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.17.2-–.16.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(b(n)=b(n-1)-4\). </p>
</div>
</div>
<!--Q10-->
<div class="os-raise-ib-pset-problem" data-content-id="70384a16-aac0-49c2-a57c-91d05f23be77" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(k(1)=12, k(n)=k(n-1)-6\)" data-solution-options='["\\(k(1)=12, k(n)=k(n)-6\\)", "\\(k(1)=12, k(n)=k(n-1)-6\\)", "\\((1)=12, k(n)=k(n-1)+6\\)", "\\(k(1)=12, 6⋅k(n)=k(n-1)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li> An arithmetic sequence \(k\) starts 12, 6, . . . and is represented by the graph: </li>
</ol>
<blockquote>
<p><img src="https://k12.openstax.org/contents/raise/resources/b9796b5a8c6fd4e1dbe3f5a42c3f01ad31965ef5" width="300"></p>
<p>Which of the following is a recursive definition for sequence \(k\) when \(n\geq2\)?</p>
</blockquote>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(k(1)=12, k(n)=k(n-1)-6\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.17.2–4.17.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(k(1)=12, k(n)=k(n-1)-6\). </p>
</div>
</div>
<!--Do not edit below this line-->
<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-encourage-response"> </div>
</div>