RRB ALP CBT I 25 Nov 2024 Shift 3 Paper

Concept:The first five multiples of $3$ form an arithmetic progression (A.P.), so their average can be found using the A.P. average formula.Explanation:The first five multiples of $3$ are: $3, 6, 9, 12, 15$.This sequence is an arithmetic progression with first term $a = 3$ and last term $l = 15$.For an A.P. with an odd number of terms, the average equals the middle term.Here, the middle term is the 3rd multiple: $3 \times 3 = 9$.Alternatively, use the standard formula: Average $= \frac{\text{Sum of terms}}{\text{Number of terms}}$.Sum of the multiples $= 3 + 6 + 9 + 12 + 15 = 45$.Total number of multiples $= 5$.Therefore, Average $= \frac{45}{5} = 9$.A direct shortcut formula for the average of the first $n$ multiples of a number $k$ is $\frac{k(n+1)}{2}$.Using $k = 3$ and $n = 5$, we get $\frac{3 \times 6}{2} = 9$.Thus, the average of the first five multiples of $3$ is $9$.Answer:The correct answer is $9$, which is option A.