The first, second and third terms of a geometric progression are 2+3, k+ 6 and k respectively. Given that all the terms of the geometric progression are positive, calculate: (1) the value of constant k, (3 marks) (ii) the sum to infinity of the progression. (3 marks) (b) The first and second terms of a progression are 4 and 8 respectively. Find the sum of the first 10 terms given that the progression is: (i) an arithmetic progression (2 marks) (ii) a geometric progression. (2 marks) (c) An arithmetic progression has first term a and the common difference d. Given that the sum of the third term and the sixth term is equal to the tenth term. The sum of the first 12 terms is - 180. Find the sum of the first 10 terms. (3 marks) (d) A television quiz show takes place every day. On day 1 the prize money is RM1000. If this is not won the price money is increased for day 2. The prize money is increased in similar way every day until it is won. The television company considered the following two different models for increasing the prize money. • Model 1: increase the price money by RM1000 each day • Model 2: increase the price money by 10% each day On each day that the prize money is not won the television company makes a donation to charity. The amount donated is 5% of the value of the prize on that day. After 40 days the prize money has still not been won. Calculate the total amount donated to charity if: (1) Model 1 is used (ii) Model 2 is used (4 marks) (3 marks)