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30 March, 08:28

The first element in an arithmetic sequence is 2. Its twenty second is 14. Find the value of n so that a (n) = 6

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  1. 30 March, 12:26
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    n = 8

    Step-by-step explanation:

    Given the nth term of an arithmetic sequence to be Tn = a + (n-1) d

    a = first term of the sequence

    n = number of terms

    d = common difference.

    Given the first element a = 2 and 22nd to be 14

    T22 = a + (22-1) d = 14

    a+21d = 14

    Substtuting a = 2 into the equation to get d

    2+21d = 14

    21d = 12

    d = 12/21

    d = 4/7

    The nth term of the sequence given a = 2 and d = 4/7 will be expressed as;

    Tn = 2 + (n-1) 4/7

    Given Tn = 6

    6 = 2 + (n-1) 4/7

    6 = 2+4/7 n - 4/7

    6-2+4/7 = 4/7 n

    32/7=4/7 n

    32 = 4n

    n = 32/4

    n = 8
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