Grade 5 questions on number patterns are presented along with their detailed step-by-step solutions and explanations.
Questions and Step-by-Step Solutions
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Question 1: Complete the pattern: 1, 4, 7, 10, __. What is the missing number?
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The numbers in the list are increasing by 3 (or adding 3) each time.
\(1\)
\(1 + 3 = 4\)
\(4 + 3 = 7\)
\(7 + 3 = 10\)
The missing number is \(10 + 3 = 13\). -
Question 2: Identify the pattern: 5, 10, 15, 20, __. What comes next?
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The numbers in the list are increasing by 5 (or adding 5) each time.
\(5\)
\(5 + 5 = 10\)
\(10 + 5 = 15\)
\(15 + 5 = 20\)
The next number is: \(20 + 5 = 25\). -
Question 3: Identify the pattern: 2, 6, 12, 20, __. What comes next?
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The pattern is given by adding consecutive even numbers (4, 6, 8, 10, ...).
\(2\)
\(2 + 4 = 6\)
\(6 + 6 = 12\)
\(12 + 8 = 20\)
The next number is: \(20 + 10 = 30\). -
Question 4: Find the missing number: 9, 7, 10, 8, 11, 9, 12, __.
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The pattern is made by subtracting 2 and adding 3.
\(9\)
\(9 - 2 = 7\)
\(7 + 3 = 10\)
\(10 - 2 = 8\)
\(8 + 3 = 11\)
\(11 - 2 = 9\)
\(9 + 3 = 12\)
The next number is: \(12 - 2 = 10\). -
Question 5: Complete the pattern: 1, 4, 9, 16, __. What is the missing number?
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The pattern is the square of the numbers 1, 2, 3, 4 ...
\(1^2 = 1 \times 1 = 1\)
\(2^2 = 2 \times 2 = 4\)
\(3^2 = 3 \times 3 = 9\)
\(4^2 = 4 \times 4 = 16\)
The missing number is: \(5^2 = 25\). -
Question 6: Identify the pattern: 8, 18, 38, 68, __. What comes next?
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The pattern is adding multiples of 10.
\(8\)
\(8 + (1 \times 10) = 8 + 10 = 18\)
\(18 + (2 \times 10) = 18 + 20 = 38\)
\(38 + (3 \times 10) = 38 + 30 = 68\)
The next term is: \(68 + (4 \times 10) = 68 + 40 = 108\). -
Question 7: Complete the pattern: 2, 3, 5, 7, 11, 13, __. What is the missing number?
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This is the list of prime numbers (2, 3, 5, 7, 11, 13, ...).
The missing number is the next prime number: 17. -
Question 8: Identify the pattern: 20, 10, 5, 2.5, __. What comes next?
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The pattern is dividing by 2 each time.
\(20\)
\(20 \div 2 = 10\)
\(10 \div 2 = 5\)
\(5 \div 2 = 2.5\)
The next number is: \(2.5 \div 2 = 1.25\). -
Question 9: Find the missing number: 36, 20, 12, 8, 6, __.
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The pattern is dividing by 2 and adding 2.
\(36\)
\(36 \div 2 + 2 = 18 + 2 = 20\)
\(20 \div 2 + 2 = 10 + 2 = 12\)
\(12 \div 2 + 2 = 6 + 2 = 8\)
\(8 \div 2 + 2 = 4 + 2 = 6\)
The missing number is: \(6 \div 2 + 2 = 3 + 2 = 5\). -
Question 10: Complete the pattern: 64, 16, 4, 1, __. What is the missing number?
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The pattern is dividing by 4 each time.
\(64\)
\(64 \div 4 = 16\)
\(16 \div 4 = 4\)
\(4 \div 4 = 1\)
The missing number is: \(1 \div 4 = 0.25\). -
Question 11: Find the missing number: 12, 27, 57, 107, 217, __.
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The pattern is doubling and adding 3.
\(12\)
\(12 \times 2 + 3 = 27\)
\(27 \times 2 + 3 = 57\)
\(57 \times 2 + 3 = 107\)
\(107 \times 2 + 3 = 217\)
The missing number is: \(217 \times 2 + 3 = 437\). -
Question 12: Find the missing number: 0, 1, 1, 2, 3, 5, 8, 13, 21, __.
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The pattern is that each number is the sum of the last two numbers.
\(0\)
\(1\)
\(1 + 0 = 1\)
\(1 + 1 = 2\)
\(2 + 1 = 3\)
\(3 + 2 = 5\)
\(5 + 3 = 8\)
\(8 + 5 = 13\)
\(13 + 8 = 21\)
The missing number is: \(21 + 13 = 34\).
Note: This pattern is called the Fibonacci sequence.