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 HigherNon-calculator
Special sequences: square, cube, Fibonacci, quadratic, geometric worksheet — GCSE Higher
MathsUKwww.geekhero.co.uk
- 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.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.
- 3.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.
- 4.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.
- 5.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.
- 6.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.
- 7.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.
- 8.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.
- 9.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.
- 10.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.
- 11.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.
- 12.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
- 13.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
- 14.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.
- 15.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.
Build your own mix at the worksheet builder.