Problems involving Geometric Progressions - Problems with Solutions

Problem 1
Do the numbers 8, 4, 2, 1 form a geometric progression?
Please, answer yes or no.
Problem 2
What is the common ratio of the geometric progression 3, -6, 12, -24, 48...?
Problem 3
Find the common ratio r of a geometric progression in which the first term is 5 and second term is 15.
Problem 4
Find the common ratio r of a geometric progression with first term -1 and second one 5.
Problem 5
Determine the common ratio r of an increasing geometric progression, for which the first term is 5 and the third term is 20.
Problem 6
Determine the common ratio r of a geometric progression with first term is 5 and forth term is -40.
Problem 7
Find the common ratio r of an alternating geometric progression [tex]{a_n}[/tex], for which [tex]a_1=125[/tex], [tex]a_2=-25[/tex] and [tex]a_3=5[/tex].
Problem 8
Find the fourth term of a geometric progression, whose first term is 2 and the common ratio is 3.
Problem 9
Let [tex]{a_n}[/tex] be a geometric progression with common ratio [tex]r=\frac{1}{3}[/tex]. If [tex]a_4=12[/tex], find [tex]a_1[/tex].
Problem 10
[tex]{a_n}[/tex] is a geometric progression. If the first term [tex]a_1=5[/tex] and the second term [tex]a_2=10[/tex], find [tex]a_6[/tex]

Problem 11
Let [tex]{a_n}[/tex] be an increasing geometric progression. If the first term [tex]a_1=2[/tex] and the fifth term [tex]a_5=162[/tex], determine [tex]a_3[/tex]
Problem 12
Let [tex]{a_n}[/tex] be a geometric progression, such that [tex]a_1=2[/tex] and [tex]r=3[/tex]. Find the sum of the first five elements.
Problem 13
Let [tex]{a_n}[/tex] be a geometric progression, defined as [tex]a_1=1[/tex] and [tex]r=5[/tex]. Find the sum [tex]a_1+a_2+a_3+a_4+a_5[/tex]
Problem 14
Find the sum of the infinite geometric series [tex]{a_n}[/tex], with first term 1 and common ratio [tex]r=\frac{1}{2}[/tex].
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