Kristina and her friends are playing a game where each player would have to pass without folding their knees, under a rope held at both ends by two other players. The height of the rope above the ground is lowered by three inches every round. How high above the ground will the rope be on the 10th round if its initial height is 40 cm?
The scenario describes an arithmetic sequence with the first term, a, (initial height) as 40 cm and the common difference, d, as -3 inches (“lowered by three inches every round”).
First, we convert 3 inches to cm, so that we have the same unit. 1 inch is approximately 2.54 cm, so 3 inches is approximately
cm.
Thus, d = -7.62 cm.
The nth term of an AP is given by
. So, the height above the ground of the rope on the 10th round is 
.
Therefore, the game will not get to the 10th round before the rope touches the ground given the information provided in the question.