Solve these tasks from the sequences:
The sides of a right triangle form an arithmetic sequence with a common difference 3. Calculate the sides of this triangle.
Prove that the equation 
has real solutions if the real numbers a, b, c are consecutive terms of an arithmetic sequence.
How many solutions does the equation have if the real numbers a, b, c are consecutive terms of a geometric sequence
In a sequence of four real numbers, the first three form a geometric sequence and the last three form an arithmetic sequence. The sum of the first and last numbers is 14, and the sum of the middle two is 12. Calculate these four numbers.
and therefore the quadratic equation will always have real solutions.
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