Find the number of terms in the sequence or the sum of the sequence as requested.
-Find the following sum: 6 + 20 + 34 + . . . + 986
A)35,204
B)35,216
C)35,222
D)35,228

Question

Quizplus · Accepted Answer

This sequence is an arithmetic sequence where each term increases by 14 (20 - 6 = 14, 34 - 20 = 14, etc.). To find the number of terms (n), we use the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms. Plugging in the values, we get $986 = 6 + (n - 1)14$. Solving for $n$, we find $n = 71$. To find the sum of the sequence, we use the formula for the sum of an arithmetic sequence: $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms. Plugging in the values, we get $S_n = \frac{71}{2}(6 + 986) = 35,216$.

Find the Number of Terms in the Sequence or the Sum