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Algebra II: Evaluating a finite arithmetic series
 This is a free lesson from our course in Algebra II In this lesson you'll learn to identify the general term and concept of summation formula for finite arithmetic series.You'll find here some examples with solution, and the instructor explains all that with the help of audio, video presentation and in own hand writing. A finite series is a series that has a sum of a finite number of terms and an infinite series is a series that has a sum of an infinite number of terms.The sum of terms of an arithmetic sequence, is called an arithmetic series.For example, the sum of the series         (i=1 to 5) [(-1)i(i2)] is -15. The sum of first n terms of an arithmetic series is given by         Sn = n/2(a1 + a2), where a1 is the first term and an is the nth term of the sequence. (More text below video...)
Other useful lessons:
 Understanding sequence and series Finite geometric series Summation formulae for finite and infinite geometric series
(Continued from above) For example, the sum of the arithmetic series (n=5 to 14) (-2n+3) is -160.  Now let us go over further:
If a is the first term and d is the common difference, then arithmetic progression (A. P) is denoted by
a, a + d, a + 2d, a + 3d, a + 4d, ..., a + (n - 1)d
and the general expression can be written as,
Tr = a + (r - 1)d.
The common difference 'd' is calculated by subtracting any term from the subsequent term. E.g. the 10th term of A. P. 1, 4, 7, 10 ... =1+(10-1)3=1+(9)3=1+27= 28.
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