<s>[INST] Find the next term in the sequence. $\frac{7}{3},\frac{35}{6},\frac{121}{12},\frac{335}{36},\ldots $ $\dfrac{7}{3},\dfrac{35}{6},\dfrac{121}{12},\dfrac{335}{36},\ldots $
$\bf\text{Answer}$ given is $\dfrac{865}{48}$
I found that $4^{th}$ differencess of the numbers $7,35,121,335\cdots$ are not constant .
and the second differences of the denominator drastically changes,
$3\quad 6\quad 12\quad 36\quad 48\\~\\
\quad 3\quad 6\quad 24\quad \color{red}{12}$
decimal value is also not showing any pattern.
$\frac{7}{3},\ \frac{35}{6},\ \frac{121}{12},\ \frac{335}{36},\ldots $
$2.33,\ 5.83,\ 10.08,\ 9.33,\ldots $
 [/INST] Okay so after solving a lot this is how the answer goes..
The series is 2+1/3 , 6-1/6 , 10+1/12 , 14-1/24 , 18+1/48..
Both the integral part and fractional part follow a specific sequence.
Hope This Solved Your Problem..
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