Solve the problem.
-Find the sum of the first eleven terms of the sequence $- 9 , - 1,7,15 , \ldots , 71$ where 71 is the eleventh term.
A) 349
B) 333
C) 341
D) 342

Question

Quizplus · Accepted Answer

The given sequence is an arithmetic sequence with a common difference of 8 (subtracting each term from the next shows a consistent difference of 8). The first term, $a_1$, is $-9$, and the number of terms, $n$, is 11. The sum of the first $n$ terms of an arithmetic sequence is given by $S_n = \frac{n}{2}(a_1 + a_n)$, where $a_n$ is the nth term. Since the 11th term, $a_{11}$, is 71, we can calculate the sum as $S_{11} = \frac{11}{2}(-9 + 71) = \frac{11}{2}(62) = 341$.

Solve the Problem −9,−1,7,15,…,71- 9 , - 1,7,15 , \ldots , 71−9,−1,7,15,…,71

Solve the Problem $- 9 , - 1,7,15 , \ldots , 71$