IB Maths AI SL 1.3 Geometric sequences & series

IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise recognising geometric growth in contexts like ant colonies, weekly runs, or customer acquisition, then applying uₙ, Sₙ, and inequality solving.

How this is tested

apply uₙ = u₁rⁿ⁻¹ to find a specific term or solve uₙ > threshold to find first week exceeding a value
use the geometric series sum to find when a cumulative total passes a target
sum a finite geometric series with r ≠ 1 to model cumulative effects after a change point

[Maximum number: 7]

A marathon is a race over a distance of 42.19 km .

(a)

Find the first week during which Davi runs more than 42 km .

[ 4 ]

(b)

Find the first week that the total distance that Davi has run, since the start of training, exceeds 150 km .

[ 3 ]

How this is tested

Question 1

Question 1(d)

Question 1(e)