Find the sum.
-$$3 + 4.6 + 6.2 + 7.8 + \ldots + 55.8$$
A) $999.6$
B) $77.4$
C) $1,002.8$
D) 387

Question

Quizplus · Accepted Answer

This sequence is an arithmetic sequence where each term increases by 1.6. To find the sum, we first need to determine the number of terms. The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$, 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. Rearranging to solve for $n$, we get $n = \frac{a_n - a_1}{d} + 1$. Substituting the given values ($a_n = 55.8$, $a_1 = 3$, $d = 1.6$), we find $n = \frac{55.8 - 3}{1.6} + 1 = 34$. The sum of an arithmetic sequence is given by $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms. Substituting the known values, we get $S_n = \frac{34}{2}(3 + 55.8) = 17 \times 58.8 = 999.6$.

Find the Sum 3+4.6+6.2+7.8+…+55.83 + 4.6 + 6.2 + 7.8 + \ldots + 55.83+4.6+6.2+7.8+…+55.8

Find the Sum $3 + 4.6 + 6.2 + 7.8 + \ldots + 55.8$