# Tag Info

1 vote

### When are students taught implicit and parametric representations of curves?

(Although the OP asks for USA, this answer is for maths in England and Wales, for context and comparison) In Britain, Higher tier GCSE students (age 14-16) will meet $ax+by=c$ as the equation of a ...
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### When are students taught implicit and parametric representations of curves?

I think college prep kids (your general population at a "Sister" school) will have seen this stuff. But it will not be as ingrained as polynomial differentiation or the quadratic equation. ...

### What kind of sequence is between an arithmetic and a geometric sequence?

Since a comment asked for something from practical situations: The runtime complexity of computer algorithms gives a huge variety of sequences with all kinds of growth behaviour - and understanding ...
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### What kind of sequence is between an arithmetic and a geometric sequence?

That's a fun geometric example! Mine are more combinatorial. As Justin's answer mentions, any sequence where terms grow polynomially (with degree greater than one) is an example. For example, the ...
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### What kind of sequence is between an arithmetic and a geometric sequence?

Polynomials with $\textrm{degree}>1$ grow faster than arithmetic sequences but slower than geometric sequences. More generally, after sufficiently many terms: \begin{align*} & \textrm{logarithm}...
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The hidden connection between arithmetic and geometric sequences If we stack circles on the function $y=|x|^\color{red}{1}$, the sequence of radii is geometric. (proof) If we stack circles on the ...