Study guides › Level 8 · Algebra 2

Adding a doubling list

Level 8 · Algebra 2 · for questions like “1 + 2 + 4 + … + 512 = ?”

💡 The idea

• 1 + 2 + 4 + … + 2ⁿ⁻¹ = 2ⁿ − 1. The total is always one less than the next number in the list.
• 1 + 3 + 9 + … + 3ⁿ⁻¹ = (3ⁿ − 1) ÷ 2.

✏️ Worked examples

1. 1 + 2 + 4 + … + 512: the next number would be 1,024, so the sum is 1,023.

2. 1 + 3 + 9 + 27 + 81: the next would be 243, so (243 − 1) ÷ 2 = 121.

⚠️ Watch out

• Check with a short list: 1 + 2 + 4 = 7, which is 8 − 1. ✓

🎯 Try these

1. 1 + 2 + 4 + … + 64
2. 1 + 2 + 4 + … + 1,024
3. 1 + 3 + 9 + … + 729

Answers: 1) 127 2) 2,047 3) 1,093

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