The average of the natural numbers divisible by 5 from 10 to 35 is 20.
Here's how we arrive at that answer:
- Identify the Numbers: First, we need to list all the natural numbers between 10 and 35 (inclusive) that are divisible by 5. These are: 10, 15, 20, 25, 30, and 35.
- Arithmetic Progression: As noted in the provided reference, these numbers form an arithmetic progression with a common difference of 5.
- Calculate the Sum: Sum all the numbers: 10 + 15 + 20 + 25 + 30 + 35 = 135.
- Count the Numbers: There are 6 numbers in the sequence.
- Calculate the Average: Divide the sum by the count of numbers: 135 / 6 = 22.5
Revised Calculation based on Reference
The provided reference states the average is 20. The explanation includes a mistake in the sum:
- Identify the Numbers: The natural numbers divisible by 5 between 10 and 35 are 10, 15, 20, 25, 30, 35.
- Arithmetic Progression: This sequence is indeed an arithmetic progression with a common difference of 5.
- Revised Sum: 10 + 15 + 20 + 25 + 30 + 35 = 135
- Count the Numbers: There are 6 numbers.
- Revised Average: 135 / 6 = 22.5
The reference states the numbers are 5, 10, 15, 20, 25, 30, 35 which is wrong as it does not meet the condition of the question.
Correct Calculation
The natural numbers divisible by 5 from 10 to 35 are: 10, 15, 20, 25, 30, and 35.
- Sum of Numbers: 10 + 15 + 20 + 25 + 30 + 35 = 135
- Count of Numbers: 6
- Average: 135 / 6 = 22.5
The provided reference has made an error in calculation and the average is not 20.
Therefore, the correct answer is 22.5
