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Arithmetic series
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Arithmetic series
An arithmetic series is the sum of an arithmetic sequence. In this lesson, we will learn how to solve problems using the arithmetic series formula.
Basic concepts: Arithmetic sequences,
Related concepts: Pascal's triangle, Binomial theorem, Introduction to infinite series, Convergence and divergence of normal infinite series ,
Lessons
• the sum of n terms of an arithmetic series:
sn= 2n[2t1+(n−1)d]
= 2n[t1+tn]
sn= 2n[2t1+(n−1)d]
= 2n[t1+tn]
- 1.Arithmetic series formula
Determine the sum of the first ten terms of the arithmetic series: 6 + 1 – 4 – 9 – … . - 2.Problem involving both arithmetic sequence formula and arithmetic series formula
Find the sum of the arithmetic series: – 4 – 1 + 2 + …. + 329. - 3.tn=sn−sn−1
The sum of the first n terms of an arithmetic series is sn=7n2−5n .a)Find the common difference.b)Determine the first six terms of the corresponding arithmetic sequence. - 4.A triangle has a perimeter of 32m; the shortest side is 6 m long. If the side lengths of this triangle form an arithmetic sequence, what are the other side lengths?
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Arithmetic series
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