Sum of the first 20 even numbers — Aptitude Question
Sum of the first 20 even numbers: What is the sum of the first 20 even numbers? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
What is the sum of the first 20 even numbers?
Options
- 380
- 400
- 420
- 440
Show the answer and the worked solution
Correct answer: C. 420
Worked solution
- The numbers are 2, 4, …, 40, which is 2 × (1 + 2 + … + 20).
- = 2 × (20 × 21)/2 = 20 × 21 = 420.
Answer: 420.
The idea
Sum of the first n even numbers is n(n + 1); of the first n odd numbers it is n²; of the first n naturals, n(n + 1)/2. All three come up constantly.
Shortcut. The 20 evens run 2 to 40 with average 21, so the sum is 20 × 21 = 420.
Common trap. 400 — using n² = 20², the formula for the first n odd numbers.