Find the indicated term of the following geometric sequence.
$a_n=4(0.3{)}^{n-1}$
Find $a_5$.

• A. $0.0324$
• B. $0.0097$
• C. $0.0029$
• D. $0.1620$

Answer: (A)

Verified step by step guidance

1. Identify the general term of the geometric sequence given by the formula \(a_{n} = 4(0.3)^{n-1}\).
2. Understand that to find the 5th term, \(a_5\), you need to substitute \(n = 5\) into the formula.
3. Substitute \(n = 5\) into the expression to get \(a_5 = 4(0.3)^{5-1}\).
4. Simplify the exponent: \(5 - 1 = 4\), so rewrite the term as \(a_5 = 4(0.3)^4\).
5. Calculate \((0.3)^4\) first, then multiply the result by 4 to find the value of \(a_5\).