Problem

Find the indicated term of the geometric sequence. 5th term of $4, \frac{4}{5}, \frac{4}{25}, \ldots$ Enter the 5th term of the geometric sequence. $a_{5}=\square$ (Type an integer or a simplified fraction.)

Solution

Step 1 :We are given a geometric sequence with the first term \(a_1 = 4\) and the common ratio \(r = \frac{1}{5}\). We are asked to find the 5th term of the sequence.

Step 2 :The formula for the nth term of a geometric sequence is \(a_n = a_1 * r^{(n-1)}\), where \(a_n\) is the nth term, \(a_1\) is the first term, r is the common ratio, and n is the term number.

Step 3 :Substituting the given values into the formula, we get \(a_5 = 4 * (\frac{1}{5})^{(5-1)}\).

Step 4 :Solving the equation, we find that the 5th term of the sequence is approximately 0.0064.

Step 5 :However, the question asks for an integer or a simplified fraction. Therefore, we need to convert this decimal into a fraction.

Step 6 :The 5th term of the geometric sequence as a fraction is \(\frac{4}{625}\).

Step 7 :Final Answer: The 5th term of the geometric sequence is \(\boxed{\frac{4}{625}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/bzSkfDzomp/

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