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Sequences and nth Terms
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Sequences and nth Terms
Work through each question. Show your working where asked. For sequences, the first term is the term at n = 1.
Arithmetic and linear sequences
1.Is the sequence 6, 10, 14, 18, 22, … arithmetic?
- Yes
- No
2.Is the sequence 2, 6, 18, 54, 162, … arithmetic?
- Yes
- No
3.Is the sequence −3, 1, 5, 9, 13, … arithmetic? Give its common difference.
4.Find the nth term of the sequence 7, 12, 17, 22, 27, …
5.A sequence has nth term Tₙ = 4n − 3. Find the 12th term.
6.For the sequence Tₙ = 4n − 3, which term has value 53?
7.Is 146 a term of the sequence Tₙ = 3n + 8? Show how you know.
Quadratic sequences
8.For the sequence 4, 11, 22, 37, 56, … complete the difference table.
9.The sequence 4, 11, 22, 37, 56, … has a quadratic nth term of the form an² + bn + c. Use its first three terms to form three equations for a, b and c.
10.Find the nth term of the sequence 4, 11, 22, 37, 56, …
Sequence types and applications
11.Match each sequence type to the pattern that identifies it.
- Linear sequence
- Quadratic sequence
- Cubic sequence
- Geometric sequence
- Constant second differences
- Constant first differences
- Constant ratio between consecutive terms
- Constant third differences
12.A cinema adds 6 seats to each new row. The first row has 14 seats, the second has 20, and the third has 26. Write a formula for the number of seats in row n.
13.Using Tₙ = 6n + 8 for the cinema rows, how many seats are in row 18?
14.The sequence 1, 4, 9, 16, 25, … consists of square numbers. State its sequence type and explain how the differences support your answer.
15.Complete the arithmetic sequence 31, 25, 19, 13, … by writing its next term and its nth-term formula.
16.Decide whether each statement is true or false.
TrueFalse
Every arithmetic sequence has a positive common difference.
A quadratic sequence can have an nth term of the form an² + bn + c.
The sequence 3, 6, 9, 12, … has nth term 3n.
A cubic sequence has constant third differences.
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