If f(x + 1) = x² - 3x + 2, then what is f(x) equal to?

If x², x, -8 are in AP, then which one of the following is correct?

The third term of a GP is 3. What is the product of its first five terms?

The element in the i^th row and the j^th column of a determinant of third order is equal to 2(i + j). What is the value of the determinant?