IB Math AA 2021 Nov TZ0 Paper 1 SL Question 8 - Log and Sequence

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[Ravasandani]

found an easier way to solve this question:

first, we must prove that d = r, to answer part id, as you explained above!
to do that, we get three equations as you showed for d:

log8(p/27) = log8(q/p) = log8(125/q) -> when we equate the first expression to the 3rd expression, we get the ratio p/27 = 125/q
now, this can also be proven as a geometric sequence, because r will also be p/27 = 125/q -> which proves that it is a geometric sequence!

to solve for p, we can use the information that 27, p, q and 125 are consecutive terms in a geometric sequence, to set up an equation as such: 27r^3 = 125. Now, solving for r, we get that r = 5/3

so, p will equal to 27 * 5/3 = 45
and substituting this value of p into our original ratio of p/27 = 125/q, we will get 45/27 = 125/q, and solving for q, we get 75

[sambelmar]

step 1: 27 + r^3 = 125

step 2: r = 5/3

step 3: 27(5/3) = 45
45(5/3) = 75

9 marks🤣