# Problems involving Progressions: Problems with Solutions

Problem 1
The numbers $$1,b,c$$ form an arithmetic progression and the numbers $$1,b,c+1$$ form a geometric progression. Find c.
Problem 2
The numbers $$a,b,c$$ form an arithmetic progression with sum $$a+b+c=341$$, while $$a-1, b+2, c+13$$ form a geometric progression. Find the sum of the terms of the geometric progression.
Problem 3
The sequence $$a,1,b$$ is a non-constant arithmetic progression. The sequence $$1,a,b$$ is a geometric progression. Find b.
Problem 4
Between the numbers 9 and 243 are the numbers a and b, such that $$9,a,b,243$$ is a geometric progression. Find the arithmetic mean of a and b.
Problem 5
The numbers $$3,9,a$$ form an arithmetic progression. The sequence $$5,a,b$$ is a geometric progression. Find b.
Problem 6
The numbers $$2,4,x$$ form a geometric progression and the sequence $$3,x,y$$ is an arithmetic progression. Determine the value of y.

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