Questions: Given the following geometric sequence: 20,30,45, ... What is the common ratio? What is the value of a10 ?

Solution Steps

To solve the given geometric sequence problem, we need to:

1. Determine the common ratio by dividing the second term by the first term.
2. Use the formula for the nth term of a geometric sequence, \( a_n = a \cdot r^{(n-1)} \), to find the 10th term.

To find the common ratio \( r \) of the geometric sequence, we divide the second term \( a_2 \) by the first term \( a_1 \): \[ r = \frac{a_2}{a_1} = \frac{30}{20} = 1.5 \]

Using the formula for the nth term of a geometric sequence, \( a_n = a \cdot r^{(n-1)} \), we can find the 10th term \( a_{10} \): \[ a_{10} = a_1 \cdot r^{(10-1)} = 20 \cdot (1.5)^{9} \approx 768.8672 \]

Final Answer