Find the sum of the even integers between 51 and 99.

Question

Find the sum of the even integers between 51 and 99. ​

Quizplus · Accepted Answer

The even integers between 51 and 99 are 52, 54, ..., 98. This is an arithmetic sequence with the first term $a = 52$, the last term $l = 98$, and the common difference $d = 2$. To find the sum, we first need to find the number of terms $n$. Since the sequence is even numbers, we can calculate $n$ as $\frac{98 - 52}{2} + 1 = 24$. The sum of an arithmetic sequence is given by $S = \frac{n}{2}(a + l)$, substituting the values gives $S = \frac{24}{2}(52 + 98) = 12 \times 150 = 1800$.

Find the Sum of the Even Integers Between 51 and 99