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23 September, 10:55

Find an explicit formula for the following sequence, an which starts with a1=2/3. 2/3,3/4,4/5,5/6, ...

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  1. 23 September, 12:39
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    Step-by-step explanation:

    a1=2/3

    sequence is 2/3,3/4,4/5, ...

    for numerator a1=2

    d=3-2=1

    numerator of nth term=a1 + (n-1) d=2 + (n-1) * 1=2+n-1=n+1

    denominator = 1 more than numerator=n+1+1=n+2

    so an = (n+1) / (n+2)

    or for denominator a1=3, d=4-3=1

    denominator of nth term=3 + (n-1) * 1=3+n-1=n+2

    an = (n+1) / (n+2)
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