-
The sum of all even numbers between 21 and 51 is
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- 518
- 540
- 560
- 596
Correct Option: B
22 + 24 + 26 + ... + 50
= 2 (11 + 12 + 13 + .... + 25)
= 2 [(1 + 2 + 3 + ... + 25) – (1 + 2 + 3 ... + 10)]
| = 2 |  | − |  | ||
| 2 | 2 |
= 2 (325 – 55) = 2 × 270 = 540
Method 2 :
Sum of first n even numbers = n (n + 1)
∴ Required sum = Sum of 25
even numbers from 1 to 50 – sum
of 10 even numbers from 1 to 20
= 25×26 – 10 × 11 = 650 – 110
= 540
