Given information:
- Two consecutive numbers are removed from the list 1, 2, 3, ..., n.
- The arithmetic mean of the remaining numbers is 105/4.

Approach:
1. Let's assume the two consecutive numbers that are removed are x and x+1.
2. We need to find the value of n and the removed numbers x and x+1.

Solution:

Step 1: Find the arithmetic mean of the remaining numbers:
1. The sum of the numbers from 1 to n (inclusive) can be calculated using the formula: sum = (n/2)(first term + last term).
2. The first term in the given list is 1, and the last term is n.
3. So, the sum of the numbers from 1 to n is (n/2)(1 + n).

Step 2: Calculate the sum of the remaining numbers:
1. Since we removed two numbers, the sum of the remaining numbers will be reduced by (x + x+1).
2. The sum of the remaining numbers is (n/2)(1 + n) - (x + x+1).

Step 3: Find the number of remaining numbers:
1. We know that the remaining numbers are (n-2).
2. So, the sum of the remaining numbers can also be calculated as the arithmetic mean multiplied by the number of remaining numbers: (105/4)(n-2).

Step 4: Equate the two expressions for the sum of the remaining numbers:
1. Equate the two expressions obtained in Step 2 and Step 3: (n/2)(1 + n) - (x + x+1) = (105/4)(n-2).
2. Simplify the equation.

Step 5: Solve the equation:
1. Multiply the equation by 4 to eliminate the fraction: 2(n^2 + n) - 8(x + x+1) = 105(n-2).
2. Simplify and rearrange the equation to obtain a quadratic equation in terms of n: 2n^2 + 2n - 8x - 8 - 105n + 210 = 0.
3. Combine the terms to get: 2n^2 - 103n + 202 - 8x = 0.
4. This is a quadratic equation in n, and we can solve it using the quadratic formula.

Step 6: Find the values of n, x, and x+1:
1. Solve the quadratic equation using the quadratic formula: n = (-b ± √(b^2 - 4ac))/(2a), where a = 2, b = -103, and c = 202 - 8x.
2. Substitute the obtained values of n in the equation (n/2)(1 + n) - (x + x+1) = (105/4)(n-2) to find the values of x and x+1.

Step 7: Check the validity of the solution:
1. Check if the obtained values of n, x, and x+1 satisfy all the given conditions.
2. Verify that the removed