Printable · GCSE Foundation · ages 14-16
Special sequences: square, cube, Fibonacci, quadratic, geometric worksheet — GCSE Foundation
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 Foundation
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- 1.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.
- 2.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.
- 3.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.
- 4.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.
- 5.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.
- 6.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.
- 7.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
- 8.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.
- 9.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.
- 10.Which of these numbers is a cube number?
- 11.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
- 12.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.
- 13.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.
- 14.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.
- 15.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.
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