88.7k views
0 votes
The cost of drilling a well 300 metres deep is calculated from the following information:

The cost for the first metre is $20.00 and then the cost per metre increases by $2.00 for every subsequent metre.
Find:
a. the cost of boring the 300ᵗʰ metre

User Uko
by
8.3k points

1 Answer

3 votes

Final answer:

The cost of boring the 300th metre of the well, with the cost increasing by $2.00 for every subsequent metre after the first, is $618.00. This is calculated using the formula for the nth term of an arithmetic sequence.

Step-by-step explanation:

The cost of boring the 300th metre in a well where the cost increases by $2.00 for every subsequent metre after the first can be found using the concept of arithmetic sequences. The cost of the first metre is $20.00, which is the first term of the sequence, denoted by a1. The common difference, which is the amount by which each term increases, is $2.00, and this is denoted by d. The cost of the 300th metre can be calculated using the nth term formula of an arithmetic sequence, which is given by an = a1 + (n - 1)*d.

Therefore:

a300 = $20.00 + (300 - 1)*$2.00

a300 = $20.00 + 299*$2.00

a300 = $20.00 + $598.00

a300 = $618.00

The cost of boring the 300th metre is $618.00.

To find the cost of boring the 300th meter, we need to calculate the cost per meter. The cost for the first meter is $20.00. For the subsequent meters, the cost per meter increases by $2.00. So, the cost for the second meter is $22.00, the cost for the third meter is $24.00, and so on.

To find the cost of the 300th meter, we can use the formula:

cost = first meter cost + (number of meters - 1) * increase in cost per meter

For the 300th meter, the cost would be:

cost = $20.00 + (300 - 1) * $2.00 = $20.00 + 299 * $2.00 = $20.00 + $598.00 = $618.00

So, the cost of boring the 300th meter would be $618.00.

User Florent Henry
by
8.2k points