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Flip to reveal answersHow do you write consecutive integers?
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All 9 Flashcards — Consecutive integers
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Question
How do you write consecutive integers?
Answer
n, n + 1, n + 2 — they go up by 1. Use one starting letter.
Question
Prove the sum of three consecutive integers is a multiple of 3.
Answer
n + (n+1) + (n+2) = 3n + 3 = 3(n + 1) = 3 × a whole number.
Question
Why is the product of two consecutive integers even?
Answer
One of any two consecutive integers is even, and an even factor makes the product even.
Question
How do you prove a number is a multiple of k?
Answer
Take out a factor of k: write it as k × (a whole number).
Question
How do you prove something is NEVER a multiple of k?
Answer
Show it always leaves the same remainder: k × (whole) + r with r ≠ 0.
Question
Are the squares of three consecutive integers a multiple of 3 when summed?
Answer
No — the sum is 3(n² + 2n + 1) + 2, so it always leaves remainder 2.
Question
Sum of three consecutive integers = 3 × what?
Answer
3 × the middle integer (3n + 3 = 3(n + 1)).
Question
Can you prove a 'for all n' statement by testing examples?
Answer
No — examples never prove 'for all'. Use algebra (n, n + 1, …) and reason generally.
Question
First step in a consecutive-integer proof?
Answer
Name them with one letter (n, n + 1, n + 2), then add or multiply.
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Full study notes for Consecutive integers
Topic 1.6 hub
Proof
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