Sum of first 10 integers?

Explanation

• Use the formula n(n + 1)/2 with n = 10: (10 × 11)/2 = 110/2 = 55.
• Pairing shows why it works: 1 + 10, 2 + 9, 3 + 8, 4 + 7 and 5 + 6 each total 11, and five elevens make 55.
• Option A 45 is the sum of the first 9 integers, so it leaves out the final 10.
• The same formula gives 5050 for the first 100 integers, the well-known Gauss result.
• Related shortcuts: the first n odd numbers add to n², and the first n even numbers add to n(n + 1).
• Sum of natural numbers MCQs appear in almost every NTS maths section, so this formula is worth memorising.