Find the sum of the arithmetic sequence.
-$$32,37,42,47 , \ldots , 87$$
A) 92
B) 714
C)684
D) 694

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. Here, $a_1 = 32$, $a_n = 87$, and the common difference $d = 5$. To find $n$, we use the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $87 = 32 + (n - 1)5$. Solving for $n$, we find $n = 12$. Substituting $n = 12$, $a_1 = 32$, and $a_n = 87$ into the sum formula, we get $S_n = \frac{12}{2}(32 + 87) = 6 \times 119 = 714$.

Find the Sum of the Arithmetic Sequence 32,37,42,47,…,8732,37,42,47 , \ldots , 8732,37,42,47,…,87

Find the Sum of the Arithmetic Sequence $32,37,42,47 , \ldots , 87$