Find the indicated term of the following geometric sequence.
$a_n=10(\frac{1}{5}{)}^{n-1}$
Find $a_4$

• A. $\frac{2}{125}$
• B. $\frac{2}{25}$
• C. $\frac{8}{25}$
• D. $\frac{2}{625}$

Answer: (B)

Verified step by step guidance

1. Identify the general term of the geometric sequence given by the formula \(a_{n} = 10 \left( \frac{1}{5} \right)^{n-1}\).
2. Substitute \(n = 4\) into the formula to find the fourth term \(a_4\): \(a_4 = 10 \left( \frac{1}{5} \right)^{4-1}\).
3. Simplify the exponent: \(4 - 1 = 3\), so rewrite the term as \(a_4 = 10 \left( \frac{1}{5} \right)^3\).
4. Calculate the power of the fraction: \(\left( \frac{1}{5} \right)^3 = \frac{1^3}{5^3} = \frac{1}{125}\).
5. Multiply the coefficient by the fraction: \(10 \times \frac{1}{125} = \frac{10}{125}\), then simplify the fraction to its lowest terms.