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19 June, 09:31

Find an expression for the nth term (tn) in each of the following sequences:

t2 = 9; t4 = 25

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  1. 19 June, 13:10
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    The expression for the nth term is Tn = 8n - 7

    Step-by-step explanation:

    Here, we are to find an expression for the nth term of the sequence.

    Mathematically, the nth term of an arithmetic sequence can be expressed as;

    Tn = a + (n-1) d

    for T2, the equation is

    a + d = 9

    for T4, the equation is

    a + 3d = 25

    we can substitute the equation of T2 into T4 but we first need to rewrite T4

    a + d + 2d = 25

    9 + 2d = 25

    2d = 25 - 9

    2d = 16

    d = 16/2

    d = 8

    now since a + d = 9

    a = 9-d

    a = 9-8

    a = 1

    So the expression for the nth term would be;

    1 + (n-1) 8

    1 + 8n - 8

    = 8n - 8+1

    = 8n - 7
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