Sequences & Patterns

5 minQuiz at the end

Types of Sequences

Arithmetic Sequences

An arithmetic sequence has a constant common difference between consecutive terms.

3, 7, 11, 15, … β€” common difference: +4

Geometric Sequences

A geometric sequence has a constant common ratio between consecutive terms.

3, 6, 12, 24, … β€” common ratio: Γ—2

Finding the nth Term of an Arithmetic Sequence

Formula: aβ‚™ = a + (n-1)d

Where:

  • a = first term
  • d = common difference
  • n = position number

For 5, 8, 11, 14… (a = 5, d = 3): aβ‚™ = 5 + (n-1)Γ—3 = 5 + 3n - 3 = 3n + 2

Check: n=1 β†’ 3(1)+2=5 βœ“, n=2 β†’ 3(2)+2=8 βœ“

Finding a Specific Term

10th term of 4n-1: 4(10)-1 = 39

Term-to-Term vs Position-to-Term

  • Term-to-term rule: +4 each time
  • Position-to-term rule (nth term): tells you the value at any position directly

The nth term is more powerful β€” it lets you find the 100th term without listing 99 terms first.