23.) company a pays $23,000 yearly with raises of $1800 per year. company b pays $30,000 yearly with raises…

23.) company a pays $23,000 yearly with raises of $1800 per year. company b pays $30,000 yearly with raises of $1300 per year. which company will pay more (by how much) on the tenth year of employment?
Answer
Explanation:
Step1: Calculate Company A's pay in 10th year
We use the arithmetic - sequence formula $a_n=a_1+(n - 1)d$, where $a_1$ is the initial pay, $n$ is the number of years, and $d$ is the annual raise. For Company A, $a_1 = 23000$, $n = 10$, and $d=1800$. $a_{10}=23000+(10 - 1)\times1800=23000 + 9\times1800=23000+16200=39200$.
Step2: Calculate Company B's pay in 10th year
For Company B, $a_1 = 30000$, $n = 10$, and $d = 1300$. Using the same arithmetic - sequence formula $a_n=a_1+(n - 1)d$. $a_{10}=30000+(10 - 1)\times1300=30000+9\times1300=30000 + 11700=41700$.
Step3: Find the difference
Subtract Company A's pay from Company B's pay in the 10th year. $41700−39200 = 2500$.
Answer:
Company B will pay $2500$ more.