Sequences

Arithmetic Sequences (Basics)

100

What is the name of the constant difference between consecutive terms denoted by the letter d

common difference

200

Find the next term: 3, 7, 11, 15, ___

19

300

Find the common difference: 12, 9, 6, 3, ___

-3

400

Find the 10th term: 2, 5, 8, …

29

500

Write an explicit formula for: 4, 9, 14, 19, …

What is a_n= 4 + 5(n-1)

Arithmetic Applications

100

A sequence starts at 10 and increases by 4. Find the 5th term

26

200

Find the sum of the first 5 terms: 2, 6, 10, 14, …

50

300

A theater has 20 seats in the first row and adds 3 seats per row. How many seats in row 10?

What is 47

400

Find the sum of the first 20 terms if a₁=5  and d=2

480

500

Find n if a_n=50 , a₁=2 , and d=4

n = 13

Geometric Sequences (Basics)

100

What is term of the constant ratio between consecutive terms denoted by r

Common Ratio

200

Find the next term: 2, 6, 18, 54, ___

162

300

Find the common ratio: 81, 27, 9, 3, ___

1/3

400

Find the 6th term: 3, 6, 12, …

96

500

Write an explicit formula for: 5, 10, 20, 40, …

a_n=5(2)^n-1

Geometric Applications

100

A sequence starts at 4 and multiplies by 3 each time. Find the 4th term.

108

200

Find the sum of the first 4 terms: 2, 4, 8, 16

30

300

A bacteria culture triples every hour. If it starts with 5 bacteria, how many after 3 hours?

135

400

Find the sum of the first 5 terms if a₁= 3 and r = 2

93

500

Find n if a_n=162 , a₁=2 , and r =3

n = 5

Mixed / Challenge

100

Is this arithmetic or geometric? 7, 14, 28, 56

geometric

200

Is this arithmetic or geometric? 5, 9, 13, 17

Arithmetic

300

Find the 8th term: 1, 3, 9, 27, …

2187

400

Find the sum of the first 6 terms: 1, 2, 4, 8, …

63

500

A sequence is both arithmetic and geometric. What must it be?

constant sequence