What is the 9th term of the geometric sequence 4, −20, 100, …? −312,500 −12,500 62,500 1,562,500

First, we are going to find the common ratio of our geometric sequence using the formula: . For our sequence, we can infer that  and . So lets replace those values in our formula:



Now that we have the common ratio, lets find the  explicit formula of our sequence. To do that we are going to use the formula: . We know that ; we also know for our previous calculation that . So lets replace those values in our formula:


Finally, to find the 9th therm in our sequence, we just need to replace  with 9 in our explicit formula:




We can conclude that the 9th term in our geometric sequence is 1,562,500