Find the average of all the numbers between 6 and 34 which are divisible by 5.

### Concept & Logic When a sequence of numbers forms an Arithmetic Progression (AP) with a constant difference, the average (mean) is simply the mathematical midpoint of the series. $$Average = \frac{First\ Term + Last\ Term}{2}$$ ### Step-by-Step Solution * **Given:** We need numbers between 6 and 34 that are perfectly divisible by 5. * **Deduction:** The first multiple of 5 after 6 is 10. The last multiple of 5 before 34 is 30. * The complete valid sequence is: 10, 15, 20, 25, 30. * Since the common difference is a constant 5, this is an AP. * **Calculation:** Apply the average formula using the first valid term (10) and last valid term (30). * $Average = \frac{10 + 30}{2} = \frac{40}{2} = 20$. ### Exam Strategy & Shortcut For any evenly spaced set of numbers, never calculate the total sum. Just identify the first term and the last term, add them together, and divide by 2. It saves massive amounts of time on large sets. ### Common Pitfall A standard error is manually adding all terms together $(10 + 15 + 20 + 25 + 30)$ and making an arithmetic calculation mistake. Always default to the AP boundary shortcut to avoid unnecessary addition. ### Final Answer **Therefore, the correct answer is 20.**