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10 September, 19:13

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

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  1. 10 September, 19:21
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    The sum of arithmetic series is given by:

    Sn=n/2 (a1+an)

    where:

    n=number of terms

    a1=first term

    an=nth term

    but

    n=18, an=275, Sn=4185

    plugging the values in the formula we get:

    4185=18/2 (a1+275)

    simplifying this we get:

    4185=9 (a1+275)

    dividing through by 9 we get:

    465=a1+275

    thus

    a1=465-275

    a1=190

    Answer: first number is 190
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