The 1st, 3rd and 4th terms of a proportion are 12, 8 and 14 respectively. Find the 2nd term.

The correct answer is 21

Let the 2nd term be $x$.

Thus we have, 12:$x$ :: 8:14

⇒ $\dfrac{12}{x}$ = $\dfrac{8}{14}$

⇒ $\dfrac{12}{x}$ = $\dfrac{4}{7}$

∴ $x$ = $\dfrac{12 × 7}{4}$ = 21

Hence the 2nd term is 21.