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.


• arithmetic sequence: a sequence with a common difference between successive terms
• The nth term, tn{t_n} ,of an arithmetic sequence:
tn=t1+(n1)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, … .
    Identify the common difference.

    Determine the seventh term of the sequence.

    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
    t4=14 t_4=14, t10=32t_{10}=32

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

  • 3.
    Three consecutive terms of an arithmetic sequence are written in the form:
    Solve for the value of x.