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.
part Higher
Special sequences: square, cube, Fibonacci, quadratic, geometric worksheet — GCSE Higher
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- 1.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.
- 2.The nth term of a geometric sequence is given by aₙ = 3 × 2ⁿ⁻¹. Work out the position of the first term that is greater than 1,000.
- 3.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.
- 4.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.
- 5.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.
- 6.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.
- 7.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.
- 8.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.
- 9.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.
- 10.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.
- 11.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.
- 12.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
- 13.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
- 14.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.
- 15.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.
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