Pattern recognition

Pattern recognition finds the rule behind a sequence by looking at differences, ratios or pictures. Triangular numbers count dots in triangles: 1, 3, 6, 10, 15, …

• •• •••Pattern recognition

📐 Formula

Tₙ = 1 + 2 + … + n = n(n + 1)/2

✏️ Worked example

The 5th triangle has 1 + 2 + 3 + 4 + 5 = 15 dots.

🌍 Where it is used

Bowling pins (T₄ = 10), stacking cans, handshake problems.

❓ Quick check

Next triangular number after 10?

🏋️ Practice

EasyT₇ = ?

Answer: 28

MediumRule for 2, 5, 10, 17, 26?

Answer: n² + 1

ChallengeHow many handshakes among 6 people?

Answer: 15