I'm trying to help my grandchild with $6$th grade math homework. The question given is:
$$ 3.5,\ \ 13,\ \ 41.5,\ \ 127, \cdots $$
What are the next $3$ numbers?
2026-03-27 12:00:28.1774612828
Find the pattern sequence
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The answer that the teacher probably wants is given in the comments. Through inspection, it appears that the teacher expects the student to notice that each term is generated by multiplying the previous term by $3$ and then adding $2.5$. But as also noted in the comments, there are are more complex patterns that fit this sequence, and could result in a different answer.
Another possibility, if your grandchild is feeling brave, is to show the following graph, and offer an explanation:
"I conjectured that these were measurements taken at some regular interval. So I plotted their base ten logarithms and extrapolated. It appears that that the next measurement would be $~10^{2.6}$ which is about $398$."
Sadly, this response may merit your grandchild a D in Math 6, but an A in Physics 11.
(BTW, the response the teacher may want for the next number is $383.5$, so this is pretty close, but to be fair, my graph seems to hit the point closer to $2.7$. We're largely having some fun here, which is what math is for, right?
It would be fun to see how close this extrapolation brings us two the next two numbers.)