Study guides › Level 6 · Master

Patterns that multiply (geometric sequences)

Level 6 · Master · for questions like “3, 6, 12, 24, … What is the 8th number?”

💡 The idea

Each number is the one before it times the same amount (the ratio). To get to the nth number from the first, you multiply by the ratio n − 1 times.

nth number = first × ratioⁿ⁻¹

🪜 The steps

1. Find the ratio: second ÷ first.
2. Count the jumps: n − 1.
3. Multiply the first number by the ratio that many times.

✏️ Worked examples

1. 3, 6, 12, 24, … 8th number? The ratio is 2, with 7 jumps. 3 × 2⁷ = 3 × 128 = 384.

2. 2, 6, 18, … 6th number? The ratio is 3, with 5 jumps. 2 × 3⁵ = 2 × 243 = 486.

⚠️ Watch out

• Jumps = n − 1. The 8th number is 7 jumps from the 1st.
• Multiplying, not adding: check that the gaps keep growing.

🎯 Try these

1. 5, 10, 20, … 7th number?
2. 1, 4, 16, … 5th number?
3. 4, 12, 36, … 5th number?

Answers: 1) 320 2) 256 3) 324

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.