Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find the sum of the odd integers between 38 and 70.
A) 864
B) 810
C) 972
D) 918 Write out the first three terms and the last term of the arithmetic sequence.

Question

Quizplus · Accepted Answer

The first odd integer greater than 38 is 39, and the last odd integer less than 70 is 69. This forms an arithmetic sequence with a common difference (d) of 2. The first three terms are 39, 41, and 43, and the last term (l) is 69. To find the sum (S) of this sequence, we use the formula for the sum of an arithmetic sequence: $S = \frac{n}{2} [2a + (n-1)d]$, where n is the number of terms, a is the first term, and d is the common difference. To find n, we rearrange the formula for the nth term of an arithmetic sequence: $l = a + (n-1)d$, giving us $n = \frac{l - a}{d} + 1$. Substituting $l = 69$, $a = 39$, and $d = 2$ gives $n = \frac{69 - 39}{2} + 1 = 16$. Substituting $n = 16$, $a = 39$, and $d = 2$ into the sum formula gives $S = \frac{16}{2} [2(39) + (16-1)(2)] = 8[78 + 30] = 8[108] = 864$.

Use the Formula for the Sum of the First N