Question

1. what is the 11th term of the geometric sequence \\( (1,000,000; 100,000; 10,000; ...) \\)?

\\( a_{11} = 0.0001 \\)

\\( a_{11} = 0.001 \\)

\\( a_{11} = 1.000 \\)

\\( a_{11} = 0.100 \\)

Explanation:

⚡ Using what you learned: Geometric Sequences

Step 1: Identify the first term and common ratio

$$ a_1 = 1,000,000 $$

$$ r = \frac{100,000}{1,000,000} = 0.1 $$

Step 2: Apply the geometric sequence formula

$$ a_n = a_1 \cdot r^{n-1} $$

For \( n = 11 \):

$$ a_{11} = 1,000,000 \cdot (0.1)^{10} $$

Step 3: Calculate the value

$$ a_{11} = 10^6 \cdot (10^{-1})^{10} = 10^6 \cdot 10^{-10} = 10^{-4} = 0.0001 $$

Answer:

\( a_{11} = 0.0001 \)