Printable · GCSE Foundation · ages 14-16
Generating sequences worksheet — GCSE Foundation
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.
Generating sequences worksheet — GCSE Foundation
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- 1.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.
- 2.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.
- 3.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
- 4.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.
- 5.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
- 6.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.
- 7.Write down the first four terms of the sequence with nth term 6n − 5.
- 8.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.
- 9.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.
- 10.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?
- 11.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.
- 12.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.
- 13.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?
- 14.Which of these rules generates the sequence 6, 11, 16, 21, …?
- 15.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.
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