this is a geometry series. please explain thoroughly and step by step . this is from a math pre calculus textbook that my teacher assigned us

5. What is the value of the first term for each geometric series described? Express your answers to the nearest tenth, if necessary. a) S = 33, t = 48, r = -2 b) S = 443, n = 6, r = 6. The sum of 4 + 12 + 36 + 108 + ... + t is 4372. How many terms are in the series? 7. The common ratio of a geometric series is - and the sum of the first 5 terms is 121. a) What is the value of the first term? b) Write the first 5 terms of the series. 8. What is the second term of a geometric series in which the third term is ~ and the sixth term is _16? Determine the sum of 81 the first 6 terms. Express your answer to the nearest tenth. Apply 9. A fan-out system is used to contact a large group of people TheApply 9. A fan-out system is used to contact a large group of people. The person in charge of the contact committee relays the information to four people. Each of these four people notifies four more people, who in turn each notify four more people, and so on. a) Write the corresponding series for the number of people contacted. b) How many people are notified after 10 levels of this system? 10. A tennis ball dropped from a height of 20 m bounces to 40% of its previous height on each bounce. The total vertical distance travelled is made up of upward bounces and downward drops. Draw a diagram to represent this situation. What is the total vertical distance the ball has travelled when it hits the floor for the sixth time? Express your answer to the nearest tenth of a metre