Find the sum of the arithmetic sequence.
-1 + 3 + 5 + ... + 1,109
A) 308,025
B) 306,916
C) 309,136
D) 308,580

Question

Quizplus · Accepted Answer

The sum of an arithmetic sequence can be found using the formula $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms. Here, $a_1 = 1$, $a_n = 1109$, and the common difference $d = 2$. To find $n$, we use the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $1109 = 1 + (n - 1)2$, which simplifies to $1108 = 2(n - 1)$, and further to $554 = n - 1$, giving $n = 555$. Substituting $n = 555$, $a_1 = 1$, and $a_n = 1109$ into the sum formula gives $S_n = \frac{555}{2}(1 + 1109) = 277.5 \times 1110 = 308,025$.

Find the Sum of the Arithmetic Sequence