Question 2:Sum of a GEOMETRIC Progression is given by the formula:ACCORDING to the question (2),Sum of 'n' terms = (19531 / 625)First term 'a' = 25Last Term 'l' = (1 / 625)The general form of 'nth' term in a G.P. is:Hence, substituting the last term, we get:Substituting the value of r to power n in Sum formula we get:Hence Option (1) is the correct answer.Question 3:Given that,Now CALCULATING the 12th term we get:Hence Option (3) is the correct answer.Question 4)Given G.P = 27/8, 9/4, 3/2, ... ∞From the given series, we can see that:a = 27/8r = (27/8) ÷ (9/4) = 2/3Since 'r' < 1, the sum of infinite terms would be finite. Hence substituting in the Sum of an infinite G.P Formula, we get:Hence Option 2) is the correct answer.Question 5)Let us first split the given series into two different series 'A' and 'B'.'A' = 1/5 + 1/5² + ... ∞'B' = 1/7 + 1/7² + ... ∞Sum of both the series = Required Answer.Calculating Sum of 'A' we get:a = 1/5r = 1/5Hence Sum of 'A' = 1/4.Calculating Sum of 'B', we get:a = 1/7r = 1/7Hence Sum of 'B' = 1/6Adding both the sums, we get:Hence the sum of the given G.P. series is 5/12.Hence Option (1) is the correct answer.