Printable · GCSE Higher · ages 14-16
Special sequences: square, cube, Fibonacci, quadratic, geometric worksheet — GCSE Higher
Fifteen questions on "special sequences: square, cube, fibonacci, quadratic, geometric" — DfE statement A24. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
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Special sequences: square, cube, Fibonacci, quadratic, geometric worksheet — GCSE Higher
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- 1.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
- 2.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.
- 3.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.
- 4.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
- 5.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.
- 6.A geometric sequence has first term 4 and common ratio √2. Work out the sum of the first three terms of the sequence, giving your answer in the form a + b√2.
- 7.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.
- 8.Four sequences are shown below. Sequence P: 3, 6, 12, 24, … Sequence Q: 1, 4, 9, 16, … Sequence R: 2, 4, 8, 14, … Sequence S: 5, 10, 15, 20, … Work out which of the sequences P, Q, R and S is geometric.
- 9.A geometric sequence has first term 3 and common ratio √2. Work out the 6th term of the sequence, giving your answer in the form a√2.
- 10.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.
- 11.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.
- 12.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.
- 13.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.
- 14.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.
- 15.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.
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