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Number sequences
Dynamic arithmetic and geometric sequences, nth terms, recursive rules and contextual patterns.
Questions: 10Estimated time: 17 minutes
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Question 1out of 10
Given a₁ = 5 and aₙ = aₙ₋₁ + 6, find a9.
An arithmetic sequence has a constant difference d between consecutive terms. Next term = previous term + d. The nth term is aₙ = a₁ + (n − 1)d because reaching term n from term 1 takes n − 1 steps. d can be negative.
Question 2out of 10
An arithmetic sequence has first term 9 and difference 9. Find term 11.
An arithmetic sequence has a constant difference d between consecutive terms. Next term = previous term + d. The nth term is aₙ = a₁ + (n − 1)d because reaching term n from term 1 takes n − 1 steps. d can be negative.
Question 3out of 10
Given a₁ = 2 and aₙ = aₙ₋₁ + 4, find a8.
An arithmetic sequence has a constant difference d between consecutive terms. Next term = previous term + d. The nth term is aₙ = a₁ + (n − 1)d because reaching term n from term 1 takes n − 1 steps. d can be negative.
Question 4out of 10
A sequence has first term 8 and difference 2. What term number has value 28?
Rearrange aₙ = a₁ + (n − 1)d to n = (aₙ − a₁)/d + 1. Subtract the first term from the given value, divide by the common difference and add 1.
Question 5out of 10
Which statement correctly describes an arithmetic sequence?
An arithmetic sequence has a constant difference d between consecutive terms. Next term = previous term + d. The nth term is aₙ = a₁ + (n − 1)d because reaching term n from term 1 takes n − 1 steps. d can be negative.
Question 6out of 10
Continue the geometric sequence: 3, 9, 27, 81, 243
Each next term in a geometric sequence is the preceding term multiplied by the constant ratio q. Find q by dividing consecutive terms. The nth term is aₙ = a₁ × qⁿ⁻¹.
Question 7out of 10
Continue the arithmetic sequence: 11, 14, 17, 20, 23
An arithmetic sequence has a constant difference d between consecutive terms. Next term = previous term + d. The nth term is aₙ = a₁ + (n − 1)d because reaching term n from term 1 takes n − 1 steps. d can be negative.
Question 8out of 10
A geometric sequence has first term 1 and ratio 4. Find term 4.
Each next term in a geometric sequence is the preceding term multiplied by the constant ratio q. Find q by dividing consecutive terms. The nth term is aₙ = a₁ × qⁿ⁻¹.
Question 9out of 10
Continue the geometric sequence: 4, 8, 16, 32, 64
Each next term in a geometric sequence is the preceding term multiplied by the constant ratio q. Find q by dividing consecutive terms. The nth term is aₙ = a₁ × qⁿ⁻¹.
Question 10out of 10
The first figure has 5 elements and each next figure has 3 more. How many are in figure 4?
An arithmetic sequence has a constant difference d between consecutive terms. Next term = previous term + d. The nth term is aₙ = a₁ + (n − 1)d because reaching term n from term 1 takes n − 1 steps. d can be negative.
Time left: 00:00:00
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Sample questions
- Continue the arithmetic sequence: ___
- An arithmetic sequence has first term ___ and difference ___. Find term ___.
- A sequence has first term ___ and difference ___. What term number has value ___?
- Continue the geometric sequence: ___
- A geometric sequence has first term ___ and ratio ___. Find term ___.
Number sequences
A number sequence is an ordered list of numbers, with its nth term denoted by aₙ. In an arithmetic sequence, each term is obtained by adding a constant difference d: aₙ = a₁ + (n − 1)d.
Analysing a sequence
In a geometric sequence, the ratio of consecutive terms is constant: aₙ = a₁qⁿ⁻¹. A recursive rule uses preceding terms, while an explicit rule gives a term directly. Decide whether the context repeatedly adds the same amount or multiplies by the same factor.
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