Question

SERIES AND SEQUENCES

A submarine starts sinking and the captain calls an emergency rescue team. The emergency operator responds that they will only make a rescue mission if the submarine reaches a depth below 1 kilometre. The captain checks the submarine depth every minute. Starting at minute 0, it is at a depth of 50 metres. At minute 1 it is 230 metres and at minute 2 there it is at 395 metres. The captain quickly notices a pattern and calls the team again and tries to convince them to mount a rescue early using his knowledge of series and sequences.

a) How should he explain it mathematically?

b) After how many minutes will he know for certain that he is correct?

Answer 1