In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Geometric series:

For and r different than 1, the sum of the first n terms of a geometric series is:

1. Find the value of the following summation:

2. Calculate the series of the following arithmetic sequence:

3 - 4. Find the first term and the common difference of the arithmetic progression a_{n}, n ≥ 1, that satisfies:

First term of S_{n}:

_{1} = 3

_{1} = 5

_{1} = 6

_{1} = 8

Common difference of S_{n}:

5. Solve the equation:

6. Evaluate S_{10} for the following geometric sequence: 1, 2, 4, 8.....

7. An arithmetic progression has S_{10} = 100 and S_{30} = 900. Find S_{50}.

8. Find the value of the following summation:

9. Find the value of x if the following numbers are in a geometric sequence: x-1, x+1, x+2.

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