Final answer:
To find the total cost of excavating a 30-meter deep well with increasing costs per meter, we calculate the sum of an arithmetic series. The cost starts at 6 euros and increases by 2.5 euros per meter. The final cost is 1267.5 euros, making option c the correct answer.
Step-by-step explanation:
The question requires us to calculate the total cost of excavating a 30-meter deep well where the cost increases by 2.5 euros for each additional meter after the first. The cost for the first meter is 6 euros. The total cost can be found using an arithmetic series where the first term is 6 euros and the common difference is 2.5 euros.
To calculate the total cost, we will use the following formula for the sum of an arithmetic series: S = n/2 × [2a + (n-1) × d], where:
- S is the sum of the series,
- n is the number of terms,
- a is the first term,
- d is the common difference.
Here, n is 30 (since the well is 30 meters), a is 6 (cost of the first meter), and d is 2.5 (increase in cost per meter).
Calculating the cost:
S = 30/2 × [2×6 + (30-1)×2.5] = 15 × (12 + 72.5) = 15 × 84.5 = 1267.5 euros.
Therefore, the completed job will cost 1267.5 euros, which makes option c. 1267.50 the correct answer.