Difficult

# Problems involving Progressions: Very Difficult Problems with Solutions

Problem 1
The numbers $$a,b,c$$, in the given order, form a non-constant geometric progression. The numbers $$a,2b,3c$$ form an arithmetic progression in the given order. Find the common ratio r of the geometric progression.
Problem 2
Let $$a,b,c,d$$ be non-integer real numbers. The numbers $$a,b,c$$ in said order form an arithmetic progression. The numbers $$b,c,d$$ in said order form a geometric progression. If $$a+d=37$$ and $$b+c=36$$, find d.
Problem 3
The integer numbers $$a,b,c$$ form a geometric progression. $$a,b,c-64$$ form an arithmetic progression. $$a,b-8,c-64$$ form a geometric progression again. Find c.
Problem 4 sent by Rohit Dalal Ajanta Public School
Find sum of the first 20 terms of $$3 \times 5+6 \times 10+9\times 15...$$
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