Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
-1, 9/5, -81/25, …
To find the equation for the given sequence, we can observe that each term is related to its position in the sequence and involves powers of -1.
The sequence starts with -1 and then alternates between positive and negative terms. This suggests that the sign of each term can be represented by (-1)^(n-1), where n is the position of the term.
Next, we can observe that the numerators of the terms are all powers of 3. Starting from 0, the numerators are 3^0, 3^2, 3^4, etc. So, the numerator of the nth term can be represented by 3^(2(n-1)).
Finally, we can observe that the denominators of the terms are all powers of 5. Starting from 1, the denominators are 5^1, 5^2, 5^3, etc. So, the denominator of the nth term can be represented by 5^n.
Putting it all together, the equation for the sequence is:
(-1)^(n-1) * (3^(2(n-1))) / (5^n)