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 an, n ≥ 1, that satisfies:





First term of Sn:










Common difference of Sn:
















5. Solve the equation:

















6. Evaluate S10 for the following geometric sequence: 1, 2, 4, 8.....
















7. An arithmetic progression has S10 = 100 and S30 = 900. Find S50.
















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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