Algebra 2 Unit 6: Sequences and Series

Arithmetic and geometric sequences, explicit and recursive formulas, sigma notation, and finite and infinite series. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Arithmetic sequencesNo calculator

What is the 20th term of the arithmetic sequence $7, 11, 15, \ldots$?

1. $87$
2. $83$
3. $76$
4. $80$

Question 2

Geometric sequencesNo calculator

What is the 8th term of the geometric sequence $3, 6, 12, \ldots$?

1. $768$
2. $192$
3. $24$
4. $384$

Question 3

Arithmetic seriesNo calculator

What is the sum of the first 15 terms of the arithmetic sequence $5, 9, 13, \ldots$?

1. $990$
2. $61$
3. $465$
4. $495$

Question 4

Geometric seriesNo calculator

What is the sum of the first 7 terms of $2+6+18+\cdots$?

1. $4374$
2. $1458$
3. $2186$
4. $729$

Question 5

Infinite geometric seriesNo calculator

What is the sum of the infinite series $12+4+\frac{4}{3}+\cdots$?

1. $18$
2. $36$
3. $16$
4. The sum does not exist

Question 6

Recursive sequencesNo calculator

A sequence has $a_1=4$ and $a_n=2a_{n-1}-3$. What is $a_5$?

1. $19$
2. $11$
3. $16$
4. $35$

Question 7

Sigma notationNo calculator

Evaluate $\sum_{k=1}^{6}(3k-1)$.

1. $17$
2. $51$
3. $57$
4. $63$

Question 8

Geometric sequencesNo calculator

In a geometric sequence, $a_2=12$ and $a_5=-96$. What is the common ratio?

1. $-8$
2. $-2$
3. $2$
4. $-3$

Question 9

Arithmetic sequencesNo calculator

Which explicit formula gives the sequence $50, 46, 42, \ldots$?

1. $a_n=50-4n$
2. $a_n=54-4n$
3. $a_n=4n-54$
4. $a_n=46+4n$

Question 10

Arithmetic seriesNo calculator

Sam saves 100 dollars in the first month and 15 dollars more each month than the month before. How much has Sam saved after 12 months, in dollars?

1. $265$
2. $1365$
3. $2190$
4. $2355$

Question 11

Infinite geometric seriesNo calculator

For which common ratio $r$ does an infinite geometric series with first term 5 have a finite sum?

1. $-1.5$
2. $0.9$
3. $1$
4. $1.1$

Question 12

Geometric sequencesNo calculator

A culture starts with 50 bacteria and triples every hour. How many bacteria are there after 5 hours?

1. $12150$
2. $36450$
3. $750$
4. $4050$