Question : What is the average of the first 29 even numbers?
Option 1: 30
Option 2: 31
Option 3: 32
Option 4: 33
Correct Answer: 30
Solution :
Sum of first $n$ terms of an arithmetic progression = $\frac{n}{2}(2×\text{first term} +(n-1)× \text{common difference})$
Here, the first 29 even numbers form an AP of 29 terms with a common difference of 2 and the first term being 2.
So, the sum = $\frac{29}{2}(2×2 +(29-1)× 2) = 870$
Average = $\frac{\text{Sum of numbers}}{\text{Total numbers}}$ = $\frac{870}{29}$ = 30
Hence, the correct answer is 30.
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