Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find the sum of the odd integers between 142 and 72.
A) 3745
B) 3751
C) 7704
D) 3756

Question

Quizplus · Accepted Answer

The sum of the odd integers between 142 and 72 can be found using the formula for the sum of the first n terms of an arithmetic sequence, $S_n = \frac{n}{2}(a_1 + a_n)$, where $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms. The first odd integer after 72 is 73, and the last odd integer before 142 is 141. To find the number of odd integers, we use the formula $n = \frac{a_n - a_1}{d} + 1$, where $d$ is the common difference, which is 2 for odd integers. Substituting $a_n = 141$, $a_1 = 73$, and $d = 2$, we get $n = \frac{141 - 73}{2} + 1 = 35$. Substituting $n = 35$, $a_1 = 73$, and $a_n = 141$ into the sum formula, we get $S_n = \frac{35}{2}(73 + 141) = 3745$.

Use the Formula for the Sum of the First N