Find the sum of the even integers between 51 and 99.
A) 1,800
B) 3,675
C) 1,725
D) 3,900
E) 3,600

Question

Find the sum of the even integers between 51 and 99. ​
A) 1,800
B) 3,675
C) 1,725
D) 3,900
E) 3,600

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