Arithmetic series

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,

Lessons

• the sum of nn terms of an arithmetic series:
sn{s_n} = n2[2t1+(n1)d]\frac{n}{2}[2{t_1} + (n - 1)d]
= n2[t1+tn]\frac{n}{2}[{t_1} + {t_n}]
  • 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=snsn1t_{n}=s_{n}-s_{n-1}
    The sum of the first n terms of an arithmetic series is sn=7n25n{s_n} = 7{n^2} - 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?