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
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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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Question : The average of 4 numbers is 45. The average of the first two numbers is thrice the average of the other two numbers. What is the sum of the first two numbers?
Option 1: 122
Option 2: 105
Option 3: 125
Option 4: 135
Question : What is the average of the first 10 even numbers?
Option 1: 12
Option 2: 10
Option 3: 13
Option 4: 11
Question : The average of 20 numbers is 30 and that of the other 30 numbers is 50. What is the average of all the numbers?
Option 1: 42
Option 2: 47
Option 3: 44
Option 4: 45
Question : What is the average of the first six (positive) odd numbers each of which is divisible by 7?
Option 2: 43
Option 3: 47
Option 4: 49
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