Study guides › Level 6 · Master

Adding a long list of numbers in a row

Level 6 · Master · for questions like “What is 1 + 2 + … + 100?”

💡 The idea

Pair the first number with the last, the second with the second-to-last, and so on. Every pair adds up to the same total.

Sum = (first + last) × how many ÷ 2

🪜 The steps

1. Count the numbers. For a list going up by 1: last − first + 1.
2. Add the first and the last.
3. Multiply by how many, then halve.

✏️ Worked examples

1. 1 + 2 + … + 100: there are 100 numbers. (1 + 100) × 100 ÷ 2 = 5,050.

2. 11 + 12 + … + 30: there are 30 − 11 + 1 = 20 numbers. (11 + 30) × 20 ÷ 2 = 410.

⚠️ Watch out

• Count carefully. From 11 to 30 is 20 numbers, not 19.
• Steps bigger than 1 (like 5, 10, 15, …) work the same way. Count with: (last − first) ÷ step + 1.

🎯 Try these

1. 1 + 2 + … + 50
2. 21 + 22 + … + 40
3. 5 + 10 + 15 + … + 100

Answers: 1) 1,275 2) 610 3) 1,050

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