Arithmetic sequences

Arithmetic sequences

An arithmetic sequence (arithmetic progression) is a number sequence with a common difference between successive terms. By using the arithmetic sequence formula, we can easily find the value of a term and the common difference in the sequence.
Basic Concepts: Sigma notation, Solving systems of linear equations by elimination
Related Concepts: Pascal's triangle, Binomial theorem, Introduction to sequences, Monotonic and bounded sequences

Lessons

• arithmetic sequence: a sequence with a common difference between successive terms
• The nth term, tn{t_n} ,of an arithmetic sequence:
tn=t1+(n−1)d{t_n} = {t_1} + \left( {n - 1} \right)d
where, tn{t_n}: nth term
t1{t_1}: first term
dd : common difference
  • 1.
    Arithmetic sequence formula
    Consider the arithmetic sequence: 5, 9, 13, 17, … .
    a)
    Identify the common difference.

    b)
    Determine the seventh term of the sequence.

    c)
    Which term in the sequence has a value of 85?

  • 2.
    Determine t1,d,tnt_1,d,t_n for the sequences in which two terms are given
    a)
    t4=14 t_4=14, t10=32t_{10}=32

    b)
    t3=−14 t_3=-14, t12=−59t_{12}=-59

  • 3.
    Three consecutive terms of an arithmetic sequence are written in the form:
    1+2x,7x,3+4x1+2x,7x,3+4x
    Solve for the value of x.
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39.
Sequences and Series
39.1
Arithmetic sequences
39.2
Arithmetic series
39.3
Geometric sequences
39.4
Geometric series
39.5
Infinite geometric series
39.6
Sigma notation
39.7
Arithmetic mean vs. Geometric mean
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