Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find 1 + 3 + 5 + 7 + . . ., the sum of the first 55 positive odd integers.
A) 2970
B) 3025
C) 3029
D) 2966

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. For the given sequence, $a_1 = 1$, $n = 55$, and $a_n = 1 + 2(n-1) = 1 + 2(55-1) = 109$. Plugging these values into the formula gives $S_{55} = \frac{55}{2}(1 + 109) = \frac{55}{2}(110) = 3025$.

Use the Partial Sum Formula to Find the Partial Sum