A social welfare organisation plants saplings in the first month and
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A social welfare organisation plants 120 saplings in the first month and, in every subsequent month, it plants 85% of the number planted in the previous month. The activity continues indefinitely.
(i) Express the total number of saplings that will eventually be planted as an infinite series.
(ii) Determine whether this series is convergent and justify your answer.
(iii) Calculate the total number of saplings that will ultimately be planted.