Printable · GCSE Higher · ages 14-16
The nth term of linear and quadratic sequences worksheet — GCSE Higher
Fifteen questions on "the nth term of linear and quadratic sequences" — DfE statement A25. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
part Higher
The nth term of linear and quadratic sequences worksheet — GCSE Higher
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- 1.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.
- 2.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.
- 3.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.
- 4.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.
- 5.The nth term of a sequence is n² + 4n. Work out the term number, n, for which the term equals 45.
- 6.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.
- 7.The nth term of a sequence is n² − 2n + 5. Work out the 10th term.
- 8.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.
- 9.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.
- 10.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.
- 11.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.
- 12.The first five terms of a quadratic sequence are 6, 11, 18, 27, 38. Work out an expression, in terms of n, for the nth term.
- 13.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.
- 14.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.
- 15.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.
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