Test: Number sequences - Year 9 MCQ

A sequence is an ordered set of numbers that follow a specific pattern or rule, such as arithmetic or geometric progressions. The other options (Secret, Sequel, Sequin) do not describe a set of numbers with a pattern.

The sequence decreases by 4 each time: 28 - 4 = 24, 24 - 4 = 20, 20 - 4 = 16.
Continuing this pattern:

• 16 - 4 = 12
• 12 - 4 = 8
• 8 - 4 = 4

Thus, the next three numbers are 12, 8, 4.

Each term is obtained by doubling the previous term:

• 2 × 2 = 4
• 4 × 2 = 8
• 8 × 2 = 16
• 16 × 2 = 32
• 32 × 2 = 64
• 64 × 2 = 128

The rule is to double the previous number, making option C correct.

This sequence doubles each time: 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, so the next number is 16 × 2 = 32.

This is the Fibonacci sequence, where each term is the sum of the two previous terms:

• 1 + 1 = 2
• 1 + 2 = 3
• 2 + 3 = 5
• 3 + 5 = 8

Continuing:

• 5 + 8 = 13
• 8 + 13 = 21
• 13 + 21 = 34

Thus, the next three numbers are 13, 21, 34.

This sequence increases by 10 each time: 10 + 10 = 20, 20 + 10 = 30, 30 + 10 = 40, so the missing number is 40.

This sequence increases by 5 each time: 5 + 5 = 10, 10 + 5 = 15, 15 + 5 = 20, 25 + 5 = 30, so the sequence continues with 20 and then 30.

This sequence multiplies by 2 each time: 3 × 2 = 6, 6 × 2 = 12, 12 × 2 = 24, so the missing number is 24.

The sequence is defined by the formula Tn = 2n - 5, where n is the term number. To find the sixth term (n = 6):

T6 = 2 × 6 - 5 = 12 - 5 = 7 Thus, the sixth term is 7.

This sequence represents the squares of natural numbers: 1² = 1, 2² = 4, 3² = 9, 4² = 16, so the next term is 5² = 25.