Application of Arithmetic and Geometric Sequences and Series

Ahmed, a scientist, is writing a research paper on projectile motion. During one of his experiments, he throws a ball from a point marked as Point A, with a certain velocity in the horizontal direction. The ball travels a total horizontal direction of 0.5 meter after 1 second, 1 meters after 2 seconds, 1.5 meters after 3 seconds, and so on. The ball hits the ground after 7 seconds. Ahmed marks the point where the ball landed as Point B. Calculate the distance between Point A and B.

Last year, 150 cases were reported of a new infectious disease. It has been predicted that the number will double every year. How many cases will be reported in the seventh year?

You go to work for a company that pays $.01 the first day, $.02 the second day, $.04 the third day, and so on. If the daily wage keeps doubling, what will your total income be after working 15 days?

Luke earned $36,000 during the first year of his job at Putt-Putt Kingdom. After each year he received a 10% raise. Find his total earnings during the first five years at his job.