Question

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?

Answer 1

`6`

Explanation:

To say that `y` is inversely proportional to `x` is to say that there is some constant `k` such that `y = k/x`

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

`a_1 = 3`

`a_2 = 6 = 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`.