Series & Sequences

Terms

100

What is the difference between a common difference and a common ratio?

Common difference: the difference between successive terms in an arithmetic sequence d=t_n-t_n-1

Common ratio: the ratio of successive terms in a geometric sequence r=t_n/t_n-1

200

What is the difference between a sequence and a series?

Sequence: An ordered list of elements

Series: A sequence in which the terms are added together, not just listed.

300

Which formula should I use to find the nth term of arithmetic sequence?

What is a_n=a₁+(n-1)d

400

Does the sequence below have a common difference, a common ratio, or neither?

2, 4, 7, 11, 16, ...

Neither

500

Under what circumstances will an infinite geometric series converge?

When |r|<1

Arithmetic Sequences

100

Determine a₃₀

18,27,36,45,...,162

a₃₀=279

200

d= 3

a₁₌ 18

Find a₅

a₅=30

300

__, 7,__, __, 31

Find a_{1 &} d

What is...?

a₁= -1

d= 8

400

If a₂=8 and a₁₀=-28, Find a_1.

What is 12?

500

Find a₁₃ when a₁=8 and a₅=90

a₁₃=254

Geometric Sequences&Series

100

What is a₁₉ in the following sequence?

2,6,18

a₁₉=774,840,978

200

Determine a formula for the nth term for

1)r=5 and a₁=3

a_n=3(5)^n-1

300

Find a₂₀

350, -262.5, 196.875

a₂₀=1.5

400

Find a₉ in the following geometric sequence

-3,9,-27

a₉=-19,683

500

a₁= 1/2

a₇=32

Find r

What is 2?

Sum

100

What is the Sum of the 31^th term in this series?

2+6+10+14...

The Sum of the 31^st term is 1,922.

200

What is the Sum of the 7^th term in this series?

3+12+48...

The Sum of the 7^th term in this series is 16,383.

300

The Sum of the 5 terms in an arithmetic series is 65 and a₁=3, what is a₅?

a₅=23

400

If the Sum of a n^th term in an arithmetic series is 493, a_n= 53 and a₁=5, this is the value of n.

What is 17?

500

In an auditorium, the first row has 18 seats, the second row has 20 seats, and so forth. This is the number of seats in the last row if there 20 rows.

What is 11?

Toss Up

100

Sigma Notation is an abbreviation for this mathematical operation.

What is a sum?

200

Sigma notation is used for mathematical (sequences, series).

What is a series?

300

The sum of the expression 3x² evaluated from k=1 to 4.

What is 90?

400

Cheri loves shoes. On the first day of Spring Break, she decides to start cleaning out her closet. If Cheri had 100 pairs of shoes on the first day and each day she got rid of three pairs, how many days would it take for her to only have 7 pairs left?

What is 32 days?

500

What is the difference between a convergent and divergent infinite series? Which one can you find the sum of? And why can you NOT find the sum of both?

A convergent series will get closer and closer to a specific number. A divergent series grows larger and does not approach a specific number. 

You can only find the sum of a convergent series.

You cannot find the sum of a divergent series because the sum would grow larger as the number of terms approached infinity.