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 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.
- 2.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.
- 3.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.
- 4.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.
- 5.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.
- 6.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.
- 7.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
- 8.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.
- 9.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.
- 10.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.
- 11.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.
- 12.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.
- 13.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.
- 14.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.
- 15.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.
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