 Hello friends, let's work out the following problem. It says the charges of boring a well are rupees 15 for first meter and increase of rupees 1.50 for every subsequent meter. Find the cost of forming the 10th meter and the total cost of boring a well 60 meter D. So let's now move on to the solution We are given that the cost of boring a well are rupees 15 for the first meter the cost of Boring first meter of well is rupees 15 and we are given that the cost increases rupees 1.50 for every subsequent meter. So the cost of Boring second meter of well Will be equal to rupees 15 plus 1.50 that is rupees 16.50 similarly Cost of boring third meter of well will be rupees 16.50 plus 1.50 because cost increases rupees 1.50 for every subsequent meter So this is equal to rupees 18 point zero zero that is rupees 18 therefore The cost of boring the well for every subsequent meter Forms an AP that is arithmetic progression Where the first term is 15 because cost of boring the first meter of the well is rupees 15 Cost of boring the second meter is 16.5 cost of boring the third meter is 18 cost of boring third me fourth meter will be 19.50 and so on now We have to find the cost of forming the 10th meter of the well That is we have to find the 10th term of this AP now We know that the nx term of an arithmetic progression or AP denoted by a n is given by a plus n minus 1 into D where a is the first term and D is the common difference right now here the first term is 15 and the common difference D is 1.50 that is difference between 16.5 and 15 is 1.50 difference between 18 and 16.5 zero is 1.5 so the common difference is 1.50 now we have to find the 10th term that is a 10 will be given by 15 plus 10 minus 1 into 1.5 That is 15 plus 9 into 1.5 So this is equal to 15 plus 13.50 so a 10 is 28.50 so cost of boring Or cost of forming 10th meter is equal to rupees 28.50 You must write this formula Next we have to find the cost of boring of well 60 meter D That is we have to find the total cost of boring of well, which is 60 meter D now these are the cost of Boring a subsequent meter so now we have to find the sum of 60 terms in this AP now the sum of n terms in an AP Denoted by SN is given by n by 2 into 2a plus n minus 1 into D where n is the number of terms a is the first term D is the common difference Now we have to find the total cost of Boring a well of 60 meter D So n is 60 upon 2 into 2 into 15 plus 60 minus 1 into 1.5 60 by 2 is 30 into 30 plus 9 into 1.5 This is 30 into 30 plus 9 into 1.5 is 13.50 This is equal to 30 into 43.50 Here we had 60 minus 1 that is 59 of 59 into 1.5 is 88.50 So here we have 88 88 plus 30 is 118.50 now 30 into 118.50 is 355 so the cost of Boring a well 60 meter D is equal to rupees 3555 and also the cost of Forming the 10th meter is rupees 28.50 So this completes the question and the session by for now take care. Have a good day