Find the sum of the arithmetic sequence.
-(-6) + (-1) + 4 + 9 + ... + 39
A) 330
B) 170
C) 160
D) 165

Question

Quizplus · Accepted Answer

The given sequence is an arithmetic sequence with the first term $a_1 = -6$ and a common difference $d = 5$. The last term $a_n = 39$. To find the sum $S_n$ of the sequence, we first need to find the number of terms $n$. We can use the formula for the $n$th term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $39 = -6 + (n - 1)5$. Solving for $n$, we find $n = 10$. Now, we can use the formula for the sum of the first $n$ terms of an arithmetic sequence: $S_n = \frac{n}{2}(a_1 + a_n)$. Substituting the known values, we get $S_n = \frac{10}{2}(-6 + 39) = 5 \times 33 = 165$.

Find the Sum of the Arithmetic Sequence