📊 Part 1: Identifying Arithmetic Sequences

1. Circle whether each sequence is arithmetic or not:

a) 3, 7, 11, 15, 19, ...

Arithmetic

Not arithmetic

b) 5, 15, 45, 135, ...

Arithmetic

Not arithmetic

c) 2, 4, 6, 8, 10, ...

Arithmetic

Not arithmetic

2. For the arithmetic sequences above, find the common difference:

🔢 Part 2: Finding nth Terms of Linear Sequences

3. Find the nth term formula for the sequence: 5, 8, 11, 14, 17, ...

Remember: T_n = an + b

4. The nth term of a sequence is T_n = 3n + 2. Find:

a) The 10th term: ___________

b) The 25th term: ___________

c) Which term equals 32? ___________

5. Is 157 a term in the sequence T_n = 2n + 13? Show your working:

📈 Part 3: Quadratic Sequences

6. For the sequence 3, 8, 15, 24, 35, ... complete the difference table:

Terms: 3 8 15 24 35

1st differences: ____ ____ ____ ____

2nd differences: ____ ____ ____

7. Since the second differences are constant, this is a quadratic sequence. The general form is T_n = an² + bn + c. Using the first three terms, set up equations to find a, b, and c:

🎯 Part 4: Sequence Types and Applications

8. Match each sequence type with its characteristics:

1. Linear sequence

2. Quadratic sequence

3. Cubic sequence

A. Third differences are constant

B. First differences are constant

C. Second differences are constant

9. Sarah saves money each week. In week 1 she saves £5, week 2 she saves £8, week 3 she saves £11, and so on. Write the nth term formula for her savings:

10. Using your formula from question 9, how much will Sarah save in week 20?