Practice Sequence in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An ordered list of numbers generated by a rule, where each number has a specific position (first, second, third,...).

A pattern of numbers: first term, second term, third term, and so on.

Showing a random 20 of 50 problems.

Example 1

easy

What is the next term in

5, 10, 20, 40, \ldots

Example 2

challenge

Trace:

a=1

;

b=a

;

a=a+b

;

b=a+b

;

a=a+b

; OUTPUT

a

Example 3

medium

Find a formula for the

n

th term of

1, 4, 9, 16, 25, \ldots

and use it to find the 8th term.

Example 4

medium

Determine whether

a_n = \frac{2^n}{n!}

converges or diverges.

Example 5

easy

Find the 4th term of the sequence

a_n=2n+1

Example 6

medium

If you reorder `open file; read file; close file` to `read; open; close`, what happens at runtime?

Example 7

medium

Trace:

count=0

;

count=count+1

;

count=count*2

;

count=count+1

; OUTPUT

count

Example 8

medium

Determine whether the sequence

a_n = \frac{3n^2 + 1}{n^2 + 2}

converges or diverges. If it converges, find the limit.

Example 9

medium

For the sequence

a_n=2n+1

, what is the difference

a_{n+1}-a_n

Example 10

medium

The sequence

a_n=(-1)^n

gives

-1,1,-1,1,\ldots

. Does it converge?

Example 11

hard

A statement using

z

appears at line 3;

z

is assigned at line 7. Will the program work as written? Why or why not?

Example 12

hard

Trace:

a=1

;

b=2

;

c=3

;

a=b

;

b=c

;

c=a

. Final

a,b,c

Example 13

easy

3, 7, 11, 15, \ldots

a sequence or a series?

Example 14

medium

Trace:

x=5

;

y=10

; swap (no temp):

x=x+y

;

y=x-y

;

x=x-y

. Final

x,y

Example 15

medium

Trace:

a=2

;

b=a*a

;

c=b*a

;

d=c+b+a

; OUTPUT

d

Example 16

medium

A program reads two numbers, prints their sum, then their product. Write the sequence of 4 steps in plain pseudocode order.

Example 17

medium

Order so that account balance prints correctly: (1) print balance, (2) deposit = 50, (3) balance = balance + deposit, (4) balance = 100. Give the order.

Example 18

challenge

The Fibonacci sequence is

1,1,2,3,5,8,\ldots

with

F_{n+1}=F_n+F_{n-1}

. Show

\frac{F_{n+1}}{F_n}

approaches

\frac{1+\sqrt5}{2}

Example 19

easy

2, 2, 2, 2, \ldots

a valid sequence? What is its limit?

Example 20

easy

Trace:

a=4

;

b=a+a

;

c=b+a

. What is

c

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Related Concepts

Arithmetic Sequence Geometric Sequence Series