3) Given a geometric sequence with $a_{1}=5$ and $a_{4}=-5$, find $a_{7}$.

Step 1 ：Given a geometric sequence with \(a_{1}=5\) and \(a_{4}=-5\).

Step 2 ：A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio.

Step 3 ：We can use the formula for the nth term of a geometric sequence, which is \(a_{n}=a_{1} \times r^{(n-1)}\), where \(r\) is the common ratio.

Step 4 ：We can find the common ratio by substituting \(n=4\) and \(a_{4}=-5\) into the formula and solving for \(r\).

Step 5 ：Substituting the values, we get \( -5 = 5 \times r^{(4-1)} \). Solving this equation, we find that \(r = -1\).

Step 6 ：Once we have the common ratio, we can find \(a_{7}\) by substituting \(n=7\) and the found \(r\) into the formula.

Step 7 ：Substituting the values, we get \(a_{7} = 5 \times (-1)^{(7-1)}\).

Step 8 ：Solving this equation, we find that \(a_{7} = 5\).

Step 9 ：Final Answer: The seventh term of the geometric sequence is \(\boxed{5}\).