# Geometric Sequences

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Problem #1
Which of the following is a geometric sequence?

Problem #2
Find the common ratio of the geometric sequence $2,10,50,\cdots$

Problem #3
The nth term of a geometric sequence is $a_n=2 \times (\frac{1}{3})^{n-1}$. Calculate the ratio $\frac{a_3}{a_2} = ?$

Problem #4
What is the value of the fifth term of the geometric sequence $2,6,18, \cdots$?

Problem #5
The fifth term of a geometric sequence is 2 and the second term is 54. What is the common ratio of the sequence?

Problem #6
If in a geometric sequence $a_2 \times a_7=6$, then what is $a_3 \times a_4 \times a_5 \times a_6$?

Problem #7
If in a geometric sequence $a_2 \times a_4 = 25$ and also all the terms are positive, what is the value of $a_3$?

Problem #8
$a_n$ is the $n$th therm of a geometric sequence. Which is true?

Problem #9
If $a_5=2^7$ and $q=\frac{1}{2}$ then what is the value of $a_1$?

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