Which of the following are geometric series? Select all that apply.0.2 + 0.3 + 0.4 + 0.50.2 + 0.6 + 1.8 + 5.42 + 10 + 50 + 2502 + 4 + 6 + 822 + 20 + 18 + 1620 + 10 + 5 + 2.5Identify the value of r and a1 for each geometric series.0.2 + 0.6 + 1.8 + 5.4r = a1 = 2 + 10 + 50 + 250r = a1 = 20 + 10 + 5 + 2.5r = a1 =

Answer:second, third, and sixth options are geometric seriesStep-by-step explanation:Consider analyzing the quotient of two consecutive terms of the series a term divided the one preceding it- (do such for all terms listed) and see if there is a "common ratio" appearing for them.In the case: 0.2 + 0.6 + 1.8 + 5.4do: 0.6/0.2 = 3      1.8/0.6 = 3      5.4/1.8 = 3therefore 3 is the "common ratio" --> r = 3and the first term of the series is:  a1 = 0.2In the case: 2 + 10 + 50 + 250do: 10/2 = 5      50/10 = 5      250/50 = 5therefore 5 is the "common ratio" --> r = 5and the first term of the series is:  a1 = 2In the case: 20 + 10 + 5 + 2.5do: 10/20 = 0.5      5/10 = 0.5      2.5/5 = 0.5therefore 0.5 is the "common ratio" --> r = 0.5and the first term of the series is:  a1 = 20