Question : What is the average of the first 50 positive even numbers?
Option 1: 50.5
Option 2: 50
Option 3: 51
Option 4: 51.5
Correct Answer: 51
Solution :
Sum of n terms of an Arithmetic Progression = $\frac{n}{2}$ × (2a + (n − 1)d)
where 'a' is the first term and 'd' is a common difference.
According to the question
Sum = $\frac{n}{2}$ × (2a + (n − 1)d) = $\frac{50}{2}$ × (2 × 2 + (50 − 1) × 2)
= 25 × (4 + 98)
= 2550
Now,
Average = $\frac{\text{Sum of numbers}}{\text{total count of numbers}}$ = $\frac{2550}{50}$ = 51
Hence, the correct answer is 51.
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