Final answer:
The cost of burying 750 meters using the given cost per meter can be calculated by finding the sum of an arithmetic sequence.
Step-by-step explanation:
To find the cost of burying 750 meters using the given cost per meter, we need to calculate the total cost for each meter and then sum them up.
Given that the 1st meter costs $250, and the cost per meter increases by $50 for each additional meter, we can create an arithmetic sequence to represent the cost of each meter: $250, $300, $350, $400, ...
To find the cost of burying the 750 meters, we can use the formula for the sum of an arithmetic sequence:
S_n = (n / 2)(2a + (n - 1)d)
Where:
- S_n is the sum of the first n terms
- a is the first term
- d is the common difference
- n is the number of terms
In this case, a = 250, d = 50, and n = 750. Plugging these values into the formula, we get:
S_750 = (750 / 2)(2 * 250 + (750 - 1) * 50) = (375)(500 + 749 * 50) = 375(500 + 37,450) = 375(37,950) = $14,231,250.
Therefore, the cost of burying 750 meters is $14,231,250.