$-\dfrac{5}{3}, x \text{ and } -\dfrac{3}{5}$ are three consecutive terms of a G.P. Find the value(s) of x.

Rohit writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with the instructions that they move the chain similarly. Assuming that the chain is not broken and that it costs ₹ 10 to mail one letter, determine the amount spent on postage when the fourth set of letters is mailed.

Richard borrows ₹ 10,000 from his friend Ramesh. Ramesh asks him to return the money just by repaying ₹ 10 at first day and double the amount in the subsequent days than the each previous day continuously for 10 days. Richard thanks Ramesh for his help. Determine whether Ramesh was in loss or profit.

Case study:
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. A total of 27 flags have to be fixed at intervals of every 3 m. All the flags are kept at the position of the middle most flag. Rohan was given the responsibility of placing the flags on both the sides of the middle most flag. Rohan could carry only one flag at a time. So he carries one flag from the middle most point, places the flag at the designated place and comes back to the middle most point. He continues this for all the flags on both sides.

Based on the above information, answer the following questions:

(i) The distance covered by Rohan in placing the flags on one side of the middle most flag forms a sequence. Identify the type of sequence by writing at least the first 4 terms of the sequence.

(ii) Find the distance covered by Rohan in placing the 10^th flag and coming back to the middle most flag.

(iii) Find the total distance travelled by Rohan in fixing all the 27 flags.