# Problems involving Geometric Progressions: Problems with Solutions

Problem 1
Do the numbers 8, 4, 2, 1 form a geometric progression?
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 $${a_n}$$, for which $$a_1=125$$, $$a_2=-25$$ and $$a_3=5$$.
Problem 8
Find the fourth term of a geometric progression, whose first term is 2 and the common ratio is 3.
Problem 9
Let $${a_n}$$ be a geometric progression with common ratio $$r=\frac{1}{3}$$. If $$a_4=12$$, find $$a_1$$.
Problem 10
$${a_n}$$ is a geometric progression. If the first term $$a_1=5$$ and the second term $$a_2=10$$, find $$a_6$$

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

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