A company is to distribute $29,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.
A)$6,400, $5,800, $5,200, $4,600, $4,000
B)$6,800, $6,700, $6,300, $5,900, $4,600
C)$7,000, $6,500, $6,100, $5,700, $4,600
D)$7,000, $6,400, $5,800, $5,200, $4,600
E)$6,800, $6,600, $6,200, $5,800, $4,600

Question

Quizplus · Accepted Answer

The total bonus amount is $29,000, and the difference between each salesperson's bonus is constant. Starting from the fifth salesperson with $4,600, we can calculate backwards using the arithmetic sequence formula. The sum of an arithmetic series is given by $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the total sum, $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $S_5 = 29000$, $n = 5$, and $a_5 = 4600$. To find the common difference $d$ and the first term $a_1$, we use the given information and solve for these values, leading to the sequence $7,000, $6,400, $5,800, $5,200, $4,600, which matches option D.

A Company Is to Distribute $29,000 in Bonuses to Its