Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

Question

423 , 423/5, 423/25, ...
Write your answer using proper fractions, improper fractions, and integers.

an = _(_)^ n^ -^ 1

Answer 1

To describe the given sequence \(423, \frac{423}{5}, \frac{423}{25}, \ldots\), we can analyze the terms.

1. The first term, \( a_1 = 423 \).
2. The second term, \( a_2 = \frac{423}{5} \).
3. The third term, \( a_3 = \frac{423}{25} \).

Notice that each term can be expressed as a fraction where the denominator is a power of \(5\):

• \(5^0 = 1\) for the first term \(423\),
• \(5^1 = 5\) for the second term,
• \(5^2 = 25\) for the third term.

From this, we can see that the \(n\)-th term can be expressed as: \[ a_n = \frac{423}{5^{n-1}} \]

Thus, the equation to describe the sequence is: \[ a_n = \frac{423}{5^{n-1}} \]