# Each term of a sequence, after the first, is inversely proportional to the term preceding it. If the first two terms are 3 and 6, what is the twelfth term?

Jun 14, 2017

$6$

#### Explanation:

To say that $y$ is inversely proportional to $x$ is to say that there is some constant $k$ such that $y = \frac{k}{x}$

For our sequence that constant is $18$, since we have:

${a}_{1} = 3$

${a}_{2} = 6 = \frac{18}{3}$

Subsequent terms will alternate between $3$ and $6$, with the odd terms being $3$ and the even terms being $6$.

So the $12$th term is $6$.