Printable · GCSE Higher · ages 14-16
Generating sequences worksheet — GCSE Higher
Fifteen questions on "generating sequences" — DfE statement A23. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
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Generating sequences worksheet — GCSE Higher
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- 1.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?
- 2.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.
- 3.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.
- 4.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.
- 5.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
- 6.Which of these rules generates the sequence 6, 11, 16, 21, …?
- 7.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
- 8.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.
- 9.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
- 10.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.
- 11.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?
- 12.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.
- 13.Write down the first four terms of the sequence with nth term 6n − 5.
- 14.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.
- 15.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.
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