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48fae8e7-13e4-448a-a865-9bf352cf3e7a.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="a2ed7149-25ab-40c4-a28b-e471cbb510fe" 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>
<!--1a-->
<div class="os-raise-ib-pset-problem" data-content-id="99402f9a-a336-4a0e-a2d3-09edacc50f47" data-problem-comparator="integer" data-problem-type="input" data-solution="163">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>Find the value of each of the arithmetic sequences below. Enter your answers as an integer only. <strong> </strong>. Do not include commas or periods.</li>
<ol class="os-raise-noindent" start="1" type="a">
<li>Find the \(21^{st}\) term of a sequence where the first term is \(3\) and the common difference is \(8\).<br>
Enter your answer here: </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 163</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2 and 4.18.4. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(163\). </p>
</div>
</div>
<!--1b-->
<div class="os-raise-ib-pset-problem" data-content-id="ca8da07c-a1b2-47c5-8fc9-4f00d8795c60" data-problem-comparator="integer" data-problem-type="input" data-solution="131">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li>Find the \(30^{th}\) term of a sequence where the first term is \(–14\) and the common difference is \(5\).<br>
Enter your answer here: </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(131\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2 and 4.18.4. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(131\). </p>
</div>
</div>
<!--1c-->
<div class="os-raise-ib-pset-problem" data-content-id="59a632cd-0c67-4b5d-abab-0c35a39ba7e3" data-problem-comparator="integer" data-problem-type="input" data-solution="-79">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li>Find the \(16^{th}\) term of a sequence where the first term is \(11\) and the common difference is \(–6\).<br>
Enter your answer here: </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! –79</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2 and 4.18.4. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(–79\). </p>
</div>
</div>
<!--2a-->
<div class="os-raise-ib-pset-problem" data-content-id="39bd974f-5453-4265-8b24-c1864b65633f" data-problem-comparator="integer" data-problem-type="input" data-solution="472392">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="1">
<li>Find the value of each of the geometric sequences below. Do not use commas or spaces in your answers. Enter your answer as integers only. . Do not include commas or periods.</li>
<ol class="os-raise-noindent" start="1" type="a">
<li>Find the \(11^{th}\) term given the first term is \(8\) and the common ratio is \(3\).<br>
Enter your answer here: </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(472392\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(472392\). </p>
</div>
</div>
<!--2b-->
<div class="os-raise-ib-pset-problem" data-content-id="1ebdbd24-382d-4498-a97e-36145e5f04d2" data-problem-comparator="integer" data-problem-type="input" data-solution="3072">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li>Find the \(10^{th}\) term given the first term is \(–6\) and the common ratio is \(–2\).<br>
Enter your answer here: </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 3072</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(3072\). </p>
</div>
</div>
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="baf6f255-ad47-4bf3-8bcf-4ed32dbc4b92" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="\(a_{n}=-6+(n-1)(-2) \)" data-solution-options='["\\(a_{n}=-2+(n-1)(-6) \\)", "\\(a_{n}=-6+(n-1)(-2) \\)", "\\(a_{n}=-6+(n-1)+(-2)\\)", "\\(a_{n}=-6+(n)(-2)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="1">
<li>A sequence is defined recursively by \(f_1=-6, f_n=f_{n-1}-2\), for \(n≥2\). Which of the following gives the nth term for \(n≥0\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(a_{n}=-6+(n-1)(-2) \)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(a_{n}=-6+(n-1)(-2) \). </p>
</div>
</div>
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="38258be5-0b3a-4ef7-ab27-c604a6fdace1" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="\(a_{n}=-20+(n-1)(5)\)" data-solution-options='["\\(a_{n}=-20+(n-1)+5\\)", "\\(a_{n}=-20+(n-1)(-2)\\)", "\\(a_{n}=-20+(n-1)(5)\\)", "\\(a_{n}=5+(n-1)(-20)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="1">
<li>A sequence is defined recursively by \(f_1=-20, f_n=f_{(n-1)}+5\) for \(n≥2\). Which of the following is the nth term?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(a_{n}=-20+(n-1)(5)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(a_{n}=-20+(n-1)(5)\). </p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="6fffcf18-e6ac-4983-9fe7-1963ef7b5157" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f_n=3 \cdot 2^{n-1}\)" data-solution-options='["\\(f_n=3 \\cdot 2^{n-1}\\)", "\\(f_n=3^n\\)", "\\(f_n=3+2n\\)", "\\(f_n=3+2^n\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="1">
<li>A sequence is defined recursively by \(f_1=3\), \(f_n=2 \cdot f_{n-1}\), \(n\geq2\). Which of the following gives the nth term for \(n\geq0\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f_n=3 \cdot 2^{n-1}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(f_n=3 \cdot 2^{n-1}\). </p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="ce6668d2-9242-4870-bca6-77ffc2b01910" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(4n-7\)" data-solution-options='["\\(4n-3\\)","\\(4n-7\\)","\\(7n-4\\)","\\(3n-4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="1">
<li>A sequence of numbers is given by \(a_2=1\), \(a_3=5\), \(a_4=9\), \(a_5=13\), \(a_6=17\). Which equation can be used to find the nth term of the sequence?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(4n-7\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(4n-7\). </p>
</div>
</div>
<!--END QUESTION.-->
<!--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>
<br>
<!--Q#7-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2bf63c90-1a68-4782-b045-e292b99cda6d" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="7">
<li>A sequence of numbers is given by \(\frac{1}{27}\), \(\frac19\), \(\frac13\) 1, …. What is the equation that can be used to find the nth term of the sequence?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(a_n = \frac{1}{27}(3)^{n-1}\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#8-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d7d7cdb3-8ade-497a-ae33-6afcff2e69a2" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="8">
<li>A sequence is given by the set of numbers 5, 1, -3, -7 … What is the equation that can be used to find the \(n^{th}\) term of the sequence? </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(a_n = 5 + (n-1)(-4)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--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="d68983fe-520b-4f25-abde-5f8edccdd470" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<div class="os-raise-ib-pset-problem" data-content-id="a213731c-aa53-490d-a01a-b1b95c11851b" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="\(a_n = 1280 (\frac 14)^{n-1}\)" data-solution-options='["\\(a_n = 1280 - 960(n-1)\\)","\\(a_n = 1280 (4)^{n-1}\\)","\\(a_n = 1280 (\\frac 14)^{n-1}\\)","\\(a_n = 1280 \\div 4(n-1)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9" type="1">
<li>A sequence consists of the following terms: 1280, 320, 80, … What is the explicit formula for this sequence? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(a_n = 1280 (\frac 14)^{n-1}\) </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(a_n = 1280 (\frac 14)^{n-1}\) . </p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="4756240a-7f43-40ce-930b-8c33a8a7c052" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="\(a_n = 1 +5(n-1)\)" data-solution-options='["\\(a_n = 1 +5(n-1)\\)","\\(a_n = 1 (a_{n-1})^5\\)","\\(a_n = 5+ a_{n-1}\\)","\\(a_n = 1 + 5(a_{n-1})\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10" type="1">
<li>An arithmetic sequence consists of the terms 1, 6, 11, 16 …. If you were asked to find the \(100^{th}\) term, what is the general formula you would use to find that value efficiently? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(a_n = 1 +5(n-1)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 4.18.2–4.18.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(a_n = 1 +5(n-1)\). </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>