Question

What will the next number be? 1/2, 1/12, 1/30, ?

Answer 1

Any ideas for this @J.F ?

Answer 2

First know that we can break this down to:

1/(2*1), 1/(2*6), 1/(2*15)

That's your first hint.
Try to find a pattern with 1, 6, and 15

Answer 3

3 is a factor of 6 and 15. does this have to do with anything?

Answer 4

\(\large \begin{align} \color{black}{ \dfrac{1}{2}, \dfrac{1}{12}, \dfrac{1}{30} ,\cdot \cdot \cdot \cdot \cdot \hspace{.33em}\\~\\
\dfrac{1}{2\times 1(2\cdot 1-1)},\dfrac{1}{2\times 2(2\cdot 2-1)}, \dfrac{1}{2\times 3(2\cdot 3-1)} ,\cdot \cdot \cdot \cdot \cdot \hspace{.33em}\\~\\
\normalsize \text{nth term } ~\rightarrow \dfrac{1}{2\times n(2\cdot n-1)} \hspace{.33em}\\~\\
}\end{align}\)

Answer 5

for the next term u have to plug in \(n=4\)

Answer 6

@J.F

1 = (1)(1)
6 = (2)(3)
15 = (3)(5)