Find the number of terms in the sequence or the sum of the sequence as requested.
-Find the sum of the following arithmetic sequence. 4 + 8 + 12 + . . . + 100
A)1300
B)1250
C)156.25
D)10,000

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, $a_1 = 4$, $a_n = 100$, and the common difference $d = 4$. 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 $100 = 4 + (n - 1)4$. Solving for $n$, we find $n = 25$. Substituting $n = 25$, $a_1 = 4$, and $a_n = 100$ into the sum formula, we get $S_n = \frac{25}{2}(4 + 100) = 12.5 \times 104 = 1300$.

Find the Number of Terms in the Sequence or the Sum