Subjects algebra

Sum Even Numbers D4896E

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Sum Even Numbers D4896E


1. **State the problem:** Find the sum of all even numbers from 60 to 100 inclusive. 2. **Identify the sequence:** The even numbers from 60 to 100 are 60, 62, 64, ..., 100. 3. **Use the formula for the sum of an arithmetic series:** $$ S_n = \frac{n}{2} (a_1 + a_n) $$ where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. 4. **Find the number of terms $n$:** The common difference $d = 2$. Number of terms: $$ n = \frac{a_n - a_1}{d} + 1 = \frac{100 - 60}{2} + 1 = 20 + 1 = 21 $$ 5. **Calculate the sum:** $$ S_{21} = \frac{21}{2} (60 + 100) = \frac{21}{2} \times 160 = 21 \times 80 = 1680 $$ 6. **Final answer:** The sum of all even numbers from 60 to 100 is **1680**.