MAT Livestream 2020

Just the maths from the MAT livestream on 27 August 2020.
We're running a maths problem-solving livestream with a particular focus on Mathematics Admissions Test problems, live at www.maths.ox.ac.uk/r/mat every Thursday.
⏩ Jump to a question
0:00 Warm-up
06:05 MAT 2010 Q1B
08:13 MAT 2009 Q2
17:00 MAT 2008 Q2
Errors in this video
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Download the questions in this video at www.maths.ox.ac.uk/system/fil...

[@pragalbhawasthi1618]

Is 0,0,0, really a Geometric Progression?
Here, I think the common ratio is not defined, since 0/0 is not defined. Well, it probably just depends on the definition, but I am assuming it is OK to call it a GP as far as MAT is concerned.

[@OxfordMathematicsPlus]

Ah. I suppose I agree that the ratio of terms doesn't exist, but they are $a$, $ar$, $ar^2$ for some $a$ and some $r$. There's a common multiple? ^James

[@niramin4108]

Hi Dr James, quick question regarding the warmup: for something like 9,9,9, where the common ratio is 1 but the common difference is 0, why are we including this as a solution?

[@OxfordMathematicsPlus]

Are the numbers 9, 9, 9 in arithmetic progression? Yes, with common difference 0. Are the numbers 9, 9, 9 in geometric progression? Yes, with common ratio 1. So this is an example of three numbers that are in arithmetic progression and in geometric progression. (I think you're maybe asking "does r need to be equal to d for something to be a GP and an AP?" to which the answer is "No" :) ). ^James