Evaluating a finite arithmetic series - Watch video (Algebra II)

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 S_n = n/2(a₁ + a₂), where a₁ is the first term and a_n is the n^th term of the sequence. (More text below video...)

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(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,
T_r = a + (r - 1)d.
The common difference 'd' is calculated by subtracting any term from the subsequent term. E.g. the 10^th term of A. P. 1, 4, 7, 10 ... =1+(10-1)3=1+(9)3=1+27= 28.

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