If $ \frac{1}{a}, \frac {1}{b} , \frac{1}{c}$ are consecutive terms of an arithmetic sequence, express b in terms of a and c.

Question

If $ \frac{1}{a}, \frac {1}{b} , \frac{1}{c}$ are consecutive terms of an arithmetic sequence, where $a,b,c \in \mathbb R\setminus 0$. Express $b$ in terms of $a$ and $c$. Answer in the most simplest form.

Answer 1

$$\frac1b-\frac1a=\frac1c-\frac1b\iff\frac2b=\frac1a+\frac1c=\frac{a+c}{ac}\iff b=\cdots$$