NIMCET 2024 — Reasoning PYQ

Method 1: Using Arithmetic Progression (Shortcut Trick)

The given numbers are consecutive integers starting from $2$ up to $n$:

$$2,3,4,5,\dots ,n$$

Since the difference between any two consecutive terms is constant ($d=1$), this sequence forms an Arithmetic Progression (AP).

For any sequence in an Arithmetic Progression, the arithmetic mean (average) is calculated directly using the shortcut formula:

$$\text{Mean}=\frac{\text{First term}+\text{Last term}}{2}$$

Here:

• $\text{First term}=2$

• $\text{Last term}=n$

Substituting these values into the formula:

$$\text{Mean}=\frac{2+n}{2}=\frac{n+2}{2}$$