alleryThe Arithmetic Mean (AM) of two positive numbers $a$ and $b$ is
A$\sqrt{ab}$
B$2ab/(a+b)$
C$ab/(a-b)$
D$(a + b)/2$
Answer & Solution
Correct answer: D. $(a + b)/2$
1. Your syllabus: the Arithmetic Mean of $a$ and $b$ is half their sum.
2. $\text{AM} = \dfrac{a + b}{2}$.
3. Geometric interpretation: AM is the AVERAGE of two values — what you intuitively call the midpoint on a number line.
4. Option A is the Geometric Mean (GM). Option C is the Harmonic Mean (HM). Option D has no standard mean interpretation.
5. By the AM-GM inequality: $\text{AM} \geq \text{GM}$ with equality iff $a = b$. So AM is always the largest of the three classical means.
_Source: syllabus Mathematics, Ch 8, §8.4 (Arithmetic Mean), p. 9._
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