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

User Mrcl
by
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1 Answer

3 votes

Answer:

5050

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.

User Ashish Charan
by
7.4k points
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