Unit 1 • Lessons 1–4 (Sequences & Series) — Quiz
Investigating patterns • Arithmetic sequences • Arithmetic growth/decay • Arithmetic series
General Term \(t_n=a_1+(n-1)d\)
Find \(d\) & \(a_1\)
Linear Growth/Decay
Series \(S_n=\frac{n}{2}(2a_1+(n-1)d)\)
Series \(S_n=\frac{n}{2}(a_1+a_n)\)
Practice Set
Each question allows 2 attempts. Use the whiteboard below each problem, then click Reveal Solution if needed.
1) General Term
For \(7,12,17,22,\dots\) choose the correct explicit rule.
Common difference \(d=5\). With \(a_1=7\): \(t_n=a_1+(n-1)d=7+5(n-1)\).
2) Find a Term
For \(a_1=3\) and \(d=-2\), find \(t_{15}\).
\(t_{15}=a_1+(15-1)d=3+14(-2)=-25.\)
3) Identify \((a_1,d)\)
The sequence \(-4,-1,2,5,\dots\) is arithmetic. Which pair is correct?
Differences are \(+3\). First term is \(-4\). So \((a_1,d)=(-4,3)\).
4) Linear Decay Context
A tank has \(120\) L and loses \(3\) L each minute. Let \(a_n\) be the amount after \(n\) minutes. What is \(a_{20}\)?
\(a_n=120-3n\Rightarrow a_{20}=120-3(20)=60.\)
5) Sum of First \(n\) Terms
For \(a_1=10\) and \(d=4\), compute \(S_{20}\).
\(S_n=\frac{n}{2}\big(2a_1+(n-1)d\big)=\frac{20}{2}\big(20+19\cdot4\big)=10\cdot96=960.\)
6) Evaluate from Explicit Rule
Given \(t_n=50+7(n-1)\), find \(t_{25}\).
\(t_{25}=50+7\cdot24=50+168=218.\)
7) Find Number of Terms
If \(a_1=5\), \(d=5\), and \(a_n=50\), find \(n\).
\(a_n=a_1+(n-1)d\Rightarrow 50=5+5(n-1)\Rightarrow 45=5(n-1)\Rightarrow n=10.\)
8) Sum Using \(a_n\)
For \(a_1=7\) and \(a_{30}=64\), find \(S_{30}\).
\(S_n=\frac{n}{2}(a_1+a_n)=\frac{30}{2}(7+64)=15\cdot71=1065.\)
Progress
Score: 0/8