Arithmetic sequences

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  1. Arithmetic sequence formula
    Consider the arithmetic sequence: 5, 9, 13, 17, … .
    1. Identify the common difference.
    2. Determine the seventh term of the sequence.
    3. 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
    1. t4=14 t_4=14, t10=32t_{10}=32
    2. 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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    Topic Notes
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    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+(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