Oxford University Maths Admissions Test 2023 Question 5

University of Oxford Mathematician Dr Tom Crawford answers each Oxford Maths Admissions Test question in under 60 seconds. This is Q5 from the 2023 MAT.

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[peterhansmeier]

You can also use 3^2 instead of 3^10 and quickly confirm (a).

[Artaimus]

I'll admit I don't even understand what the question is asking on this one.

[atlas]

Can somebody please correct me if I'm wrong but I don't see how he got 11 in the exponent. Since we are adding up to 3^10 but 3^10 not included, then the first term of the solution should be According to the sum formula: Sum= a*(r^n-1)/(r-1), in our case a=3^0=1, r=3, n=10(we go from 3^0 up to 3^9) the second part should be: 1*(3^10-1)/(3-1)=(3^10-1)/2. In the end we have: (3^20-3^10)/2 - (3^10-1)/2 = (3^20-3^10-3^10+1)/2 = (3^20-2*3^10+1)/2 = (3^10-1)^2/2.

[stuffthings]

this is why i never tried for a masters degree.