Solve the problem.
-Find the sum of the first 50 integers that are exactly divisible by 3 .
A) 3,825
B) 3,675
C) 1,275
D) 3,978

Question

Quizplus · Accepted Answer

The first 50 integers divisible by 3 are 3, 6, 9, ..., 150. This is an arithmetic sequence with the first term $a_1 = 3$, the common difference $d = 3$, and the number of terms $n = 50$. The sum of an arithmetic sequence is given by $S_n = \frac{n}{2}(a_1 + a_n)$, where $a_n$ is the last term. The last term $a_n = 3 + (50-1)*3 = 150$. Thus, $S_{50} = \frac{50}{2}(3 + 150) = 25 \times 153 = 3825$.

Solve the Problem. -Find the Sum of the First 50 Integers That Are