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grade8_patterns_quiz1 draws its questions at random from a bank of 10 questions, with full worked solutions for every one.
A few of the question types, with full solutions, so you know what to expect.
What is the constant difference in the sequence \(12;\ 17;\ 22;\ 27;\ \ldots\)?
Answer: \(+5\)
\(17-12=5,\quad 22-17=5,\quad 27-22=5\)
\(\text{The same number is added each time.}\)
Find the next three terms: \(4;\ 1;\ -2;\ -5;\ \ldots\)
Answer: \(-8;\ -11;\ -14\)
\(1-4=-3\text{, so the constant difference is } -3\)
\(-5-3=-8,\quad -8-3=-11,\quad -11-3=-14\)
What is the constant ratio in the sequence \(3;\ 9;\ 27;\ 81;\ \ldots\)?
Answer: 3
\(9\div3=3,\quad 27\div9=3,\quad 81\div27=3\)
\(\text{Each term is multiplied by the same number.}\)
Find the next three terms: \(160;\ 80;\ 40;\ 20;\ \ldots\)
Answer: \(10;\ 5;\ 2.5\)
\(\text{The constant ratio is } \tfrac{1}{2} \text{ (divide by 2 each time).}\)
\(20\div2=10,\quad 10\div2=5,\quad 5\div2=2.5\)
Which best describes the sequence \(1;\ 4;\ 9;\ 16;\ 25;\ \ldots\)?
Answer: Square numbers
\(1^2=1,\quad 2^2=4,\quad 3^2=9,\quad 4^2=16,\quad 5^2=25\)
\(\text{The differences } (3,5,7,9) \text{ are not constant.}\)