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18 February, 06:43

The sum of the first and 100th terms of an arithmetic series is 101. Find the sum of the first 100 terms.

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  1. 18 February, 06:45
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    5050

    Step-by-step explanation:

    The sum of an arithmetic series is the product of the number of terms and the average value of a term. That average value can be found as the average of the first and last terms. Then for (a1 + a100) = 101, the average term is ...

    (a1 + a100) / 2 = 101/2 = 50.5

    Since there are 100 terms, the sum of them is ...

    100 * 50.5 = 5050

    The sum of the first 100 terms is 5050.
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