Sequences and Series: Algebra 2 Math Quiz – PDF Download
Ten multiple-choice questions check explicit and recursive formulas, sigma notation, series sums and money applications. Pick the single best answer; the explanation after each question shows the common mistake.
What is the common difference of the sequence graphed below?Points \((n,a_{n})\).
A\(-6\)
B\(6\)
C\(-5\)
D\(-12\)
Question 2
If \(a_{n}=3\cdot 2^{n-1}\), what is \(a_{6}\)?
A\(192\)
B\(36\)
C\(48\)
D\(96\)
Question 3
Which recursive formula generates \(5,\,15,\,45,\,135\)?
A\(a_{1}=5,\ a_{n}=a_{n-1}+10\)
B\(a_{1}=3,\ a_{n}=5a_{n-1}\)
C\(a_{1}=5,\ a_{n}=3a_{n-1}\)
D\(a_{1}=5,\ a_{n}=a_{n-1}+3\)
Question 4
What is the value of \(\sum_{k=1}^{4}(5k-1)\)?
A\(50\)
B\(46\)
C\(36\)
D\(62\)
Question 5
Find the sum of the arithmetic series \(3+7+11\) that continues with common difference 4 until its last term, 43.
A\(506\)
B\(230\)
C\(276\)
D\(253\)
Question 6
What is the sum of the first 6 terms of the geometric series \(2+6+18+54\) that continues with ratio 3?
A\(728\)
B\(1458\)
C\(1456\)
D\(364\)
Question 7
An arithmetic sequence begins \(4,\,10,\,16\) and ends with 154. How many terms does it have?
A\(25\)
B\(27\)
C\(26\)
D\(24\)
Question 8
Which sigma expression gives the terms shown in the chart?Five terms of a series.
A\(\sum_{k=1}^{5}5\cdot 2^{k}\)
B\(\sum_{k=1}^{5}5\cdot 2^{k-1}\)
C\(\sum_{k=1}^{5}5k\)
D\(\sum_{k=1}^{4}5\cdot 2^{k-1}\)
Question 9
Ethan saves $50 in week 1 and $10 more each week than the week before. How much has he saved in total after 10 weeks?
A\(\$1{,}400\)
B\(\$900\)
C\(\$1{,}000\)
D\(\$950\)
Question 10
A ball is dropped from 8 feet and rebounds to three-fourths of its previous height on each bounce. How high is the third bounce?The drop and first three bounces.
