(i)  Fare for first km = Rs. 15Fare for second km = Rs. 15+8= Rs 23Fare for third km = Rs. 23+8=31Here, each subsequent term is obtained by adding a fixed number (8) to the previous term.Hence, it is in A.P.(ii)  Let us assume, initial quantity of air =1 .....1)Therefore, quantity removed in first step =41​Remaining quantity after first step1−41​=43​ ....2)Quantity removed in second step= 43​×41​=163​Remaining quantity after second step= 43​−163​=169​ ....3)Here, each subsequent term is not obtained by adding a fixed number to the previous term.Hence, it is not an AP.(iii) Cost of digging of 1st meter =150Cost of digging of 2nd meter =150+50=200Cost of digging of 3rd meter =200+50=250Here, each subsequent term is obtained by adding a fixed number (50) to the previous term.Hence, it is an AP.(iv)  Amount in the beginning = Rs. 10000Interest at the end of 1st year @ 8% = 10000×8 Thus, amount at the end of 1st year =10000+800=10800Interest at the end of 2nd year @ 8% = 10800×8Thus, amount at the end of 2nd year =10800+864=11664Since, each subsequent term is not obtained by adding a fixed number to the previous term; hence, it is not an AP.