<s>[INST] What number comes next in the sequence $7, 16, 8, 27, 9,...$? What number comes next in this series?
$$7, 16, 8, 27, 9,...$$
I thought it was $38$, but I'm wrong.  
It is a multiple choice, and options are $27, 10, 40, 37$.  
Don't worry - I'm not cheating on anything, but helping my daughter with homework.
And I can't help her since I can't figure it out myself!
 [/INST] Another view, also giving $40$ as the next term: $2n+2;\frac{n}{2};3n+3;\frac{n}{3};4n+4;\frac{n}{4}\cdots$
\begin{align}\text{initial value}&=7\\
7*2+2&=16\\
\frac{16}{2}&=8\\
8*3+3&=27\\
\frac{27}{3}&=9\\
9*4+4&=40\\
\frac{40}{4}&=10
\end{align}
Or: $2(n+1);\frac{n}{2};3(n+1);\frac{n}{3};4(n+1);\frac{n}{4}\cdots$
\begin{align}\text{initial value}&=7\\
2(7+1)&=16\\
\frac{16}{2}&=8\\
3(8+1)&=27\\
\frac{27}{3}&=9\\
4(9+1)&=40\\
\frac{40}{4}&=10
\end{align}
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