Geometric Sequences

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Question 1
Which of the following is a geometric sequence?

Question 2
Find the common ratio of the geometric sequence [tex]2,10,50,\cdots[/tex]

Question 3
The nth term of a geometric sequence is [tex] a_n=2 \times (\frac{1}{3})^{n-1} [/tex]. Calculate the ratio [tex] \frac{a_3}{a_2} = ?[/tex]

Question 4
What is the value of the fifth term of the geometric sequence [tex] 2,6,18, \cdots [/tex]?

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

Question 6
If in a geometric sequence [tex] a_2 \times a_7=6 [/tex], then what is [tex] a_3 \times a_4 \times a_5 \times a_6 [/tex]?

Question 7
If in a geometric sequence [tex] a_2 \times a_4 = 25 [/tex] and also all the terms are positive, what is the value of [tex] a_3 [/tex]?

Question 8
[tex]a_n[/tex] is the [tex]n[/tex]th therm of a geometric sequence. Which is true?

Question 9
If [tex] a_5=2^7 [/tex] and [tex] q=\frac{1}{2} [/tex] then what is the value of [tex] a_1 [/tex]?


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