The average of the first five multiples of 3 is

### Concept & Logic The multiples of any integer follow an Arithmetic Progression (AP) since the gap between consecutive terms is constant. For an odd number of terms in an AP, the average is exactly the middle term. $$Average\ of\ AP = Middle\ Term$$ ### Step-by-Step Solution * **Given:** We need the average of the first five multiples of 3. * **Deduction:** The series is 3, 6, 9, 12, 15. * Because the sequence is an AP (common difference of 3) and has an odd number of terms (5 terms), the median and the mean are identical. * **Calculation:** The middle term of this sequence is the 3rd term. * The 3rd term is $3 \times 3 = 9$. ### Exam Strategy & Shortcut Don't write out the sequence or add the numbers. The average of the first 5 multiples of any number $k$ is just the 3rd multiple of $k$. So, $3 \times 3 = 9$. ### Common Pitfall Calculating the total sum $(3 + 6 + 9 + 12 + 15 = 45)$ and then dividing by 5. While this gives the correct answer, it consumes precious seconds that should be saved for harder questions. ### Final Answer **Therefore, the correct answer is 9.**