Proof Definitions

An integer is...

• A number that is not a decimal or a fraction

• A decimal

• A fraction

• A surd

• A negative number

Write down the definition of an even number using the variable n, where n is an integer

(a)  

Write down the definition of an odd number using the variable n, where n is an integer

(a)  

Given that n is an integer, n, n+1, n+2, n+3 is a list of

• 4 consecutive integers

• 4 consecutive numbers

• 4 consecutive odd numbers

• 4 even numbers

Given that n is an integer, the expression

n + n + 1 + n + 2

is

• The sum of 3 consecutive integers

• The sum of 3 odd numbers

• The sum of 3 consecutive even numbers

• 3 integers

Write down a fully simplified expression for the sum of 3 consecutive integers (using the variable n where n is an integer)

(a)  

Given that n is an integer, the list

2n + 1, 2n +3, 2n +5 , 2n +7

represents

• A list of consecutive odd numbers

• A list of consecutive even numbers

• A list of consecutive integers

Which of the following is a list of consecutive even numbers (there are 2 correct answers)

• 2n, 2n + 2, 2n + 4

• 2n - 2, 2n, 2n + 2

• 2n, 2n + 1, 2n + 2

• n, n+1, n + 2

• 2n + 1, 2n +3, 2n +5

Write down a full simplified expression for the sum of 3 consecutive even numbers, using n as a variable (where n is an integer)

(a)  

Given that n is an integer, which of the following could be a fully simplified expression for the sum of 3 consecutive odd integers?

• 6n + 9

• 2n + 1

• 6n + 6

• 6n