Question

A tube well is bored 800 meters deep. The 1st meter costs $250 and the cost per meter increases by $50 for every subsequent meter. Find the cost of boring the 750th meter. A) $37,250

B) $37,750
C) $38,250
D) $38,750

Answer 1

The cost of boring the 750th meter in a tube well can be found by setting up an arithmetic sequence and using the formula for the nth term. Plugging in the given values, the cost is $37,700.

Step-by-step explanation:

To find the cost of boring the 750th meter, we need to determine the cost of each meter and then sum up the costs for the first 750 meters. The cost of the 1st meter is $250, and for each subsequent meter, the cost increases by $50. So, we can set up an arithmetic sequence to represent the costs: $250, $300, $350, $400, and so on. We can use the formula for the nth term of an arithmetic sequence to find the cost of the 750th meter:

an = a1 + (n - 1)d

Where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

In this case, a1 = $250, n = 750, and d = $50. Plugging these values into the formula, we get:

a750 = $250 + (750 - 1)($50)

a750 = $250 + 749($50)

a750 = $250 + $37,450

a750 = $37,700

The cost of boring the 750th meter is $37,700.