Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find the sum of the first 55 terms of the arithmetic sequence: 2, 4, 6, 8, . . .
A)3080
B)3086
C)112
D)3135

Question

Quizplus · Accepted Answer

The sum of the first n terms 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. For this sequence, $a_1 = 2$, the common difference $d = 2$, and $n = 55$. The nth term $a_n = a_1 + (n-1)d = 2 + (55-1) \times 2 = 110$. Thus, $S_{55} = \frac{55}{2}(2 + 110) = 27.5 \times 112 = 3080$.

Use the Formula for the Sum of the First N