Suppose $a,\ b,\ c$ are in AP, then prove that $b=\frac{a+c}{2}$.
Given: $a,\ b,\ c$ are in A.P.
To do: To prove that $b=\frac{a+c}{2}$.
Solution:
$\because a,\ b,\ c$ are in A.P.
$\Rightarrow b-a=c-b$
$\Rightarrow b+b=a+c$
$\Rightarrow 2b=a+c$
$\Rightarrow b=\frac{a+c}{2}$
Hence proved.
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