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Arithmetic Progression

If a,A,b ar...

Question

If $a, A, b$ are in arithmetic progression, prove that $A = \frac{a + b}{2}$ .

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Solution

$a, A, b$ are in arithmetic progression
$\Rightarrow T_{2} - T_{1} = T_{3} - T_{2}$
$∴$ $A - a = b - A$
$A + A = b + a$
$2 A = a + b$
$\frac{a + b}{2}$
Hence proved.

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