Adding a Sequence of Numbers

Below we will cover a math trick to add a sequence in the form: 1 + 2 + ... + n:

Look at sequence 1 + 2 + ... + 14 = ?.

• Multiply the last number in the sequence (14) by 1 number higher (15). Then divide by 2.
  • (14 * 15) / 2 = 105.
  • To make the math easier you can simplify to 7 * 15 = 105.

ANSWER is 105.

Look at sequence 2 + 3 + ... + 31 = ?.

• Multiply the last number in the sequence (31) by 1 number higher (32). Then divide by 2.
  • (31 * 32) / 2 = ?.
  • Simplify to 31 * 16 = 496
  • Use the FOIL Method if you need a trick to multiply two digit numbers.
• Subtract 1 from 496 since the sequence started with 2.

ANSWER is 495.

Watch the math video below for a detailed explanation!

Practice Math Problems

1. 1 + 2 + ... + 24 = ?
2. 1 + 2 + ... + 8 = ?
3. 1 + 2 + ... + 41 = ?
4. 2 + 3 + ... + 37 = ?