Find the common difference $d$ and the nth term $a_{n}$ of the arithmetic sequence whose 7 th term is -20 and 11 th term is -40 . The common difference $d$ of the arithmetic sequence is $\square$. (Type an integer or a fraction.) The $n$th term $a_{n}$ of the arithmetic sequence is $\square$. (Simplify your answer.)

Step 1 ：Given an arithmetic sequence where the 7th term \(a_{7}=-20\) and the 11th term \(a_{11}=-40\), we are asked to find the common difference \(d\) and the nth term \(a_{n}\) of the sequence.

Step 2 ：The common difference \(d\) in an arithmetic sequence is the difference between any two successive terms. Therefore, we can find \(d\) by subtracting the 7th term from the 11th term and dividing by the difference in their positions: \(d = (a_{11} - a_{7}) / (11 - 7)\)

Step 3 ：Substitute the given values into the formula: \(d = (-40 - (-20)) / (11 - 7)\)

Step 4 ：Simplify the expression to find the common difference: \(d = -5\)

Step 5 ：The formula for the nth term of an arithmetic sequence is given by: \(a_n = a_1 + (n - 1) * d\). However, we don't know the first term \(a_1\) directly, but we can express it in terms of \(a_7\) and \(d\): \(a_1 = a_7 - (7 - 1) * d\)

Step 6 ：Substitute the given values into the formula: \(a_1 = -20 - (7 - 1) * -5\)

Step 7 ：Simplify the expression to find the first term: \(a_1 = 10\)

Step 8 ：Now we can express the nth term \(a_n\) in terms of \(a_1\) and \(d\): \(a_n = 10 + (n - 1) * -5\)

Step 9 ：Final Answer: The common difference of the sequence is \(\boxed{-5}\) and the nth term of the sequence is \(\boxed{10 - 5(n - 1)}\)