Grade 12 Maths: Patterns and Sequences Cheat
Sheet
■ Arithmetic Sequences
General Term: T■ = a + (n - 1)d
- a = first term
- d = common difference (T■ - T■)
- Linear pattern (constant difference between terms)
Sum of n terms: S■ = (n/2)[2a + (n - 1)d]
■ Geometric Sequences
General Term: T■ = ar■■¹
- a = first term
- r = common ratio (T■ ÷ T■)
- Exponential pattern (each term multiplied by r)
Sum of n terms:
If r ≠ 1: S■ = a(1 - r■)/(1 - r) or S■ = a(r■ - 1)/(r - 1) (if r > 1)
Infinite Sum (|r| < 1): S∞ = a / (1 - r)
■ Common Tricks & Tips
- Always check the difference (d) or ratio (r) between terms.
- Use the formula when you see 'find the 10th term' or 'sum of first 20 terms'.
- Watch out for word problems — translate them to equations.
- Arithmetic: Graph is a straight line. Geometric: Graph grows or decays exponentially.
■ Example Questions
1. Find the 10th term of the sequence: 3, 7, 11, ...
→ T■ = a + (n - 1)d = 3 + (10 - 1)×4 = 3 + 36 = 39
2. Find the sum of the first 5 terms of: 2, 6, 18, ...
→ Geometric: a = 2, r = 3 → S■ = 2(1 - 3■)/(1 - 3) = 2(1 - 243)/-2 = 242