Algebra
# Arithmetic Progressions

Mary and Tina are hired for a new job with a base salary of $30,000 per year. Each year, Mary receives a $2,000 raise, while Tina only receives a $500 raise.

After 5 years have elapsed (so that each of them has received 5 raises), how much greater is Mary’s yearly salary than Tina’s?

On Day 1 starting at a new job, John is paid $20 and Jack is paid $32. Every subsequent day, John is paid $3 more than the previous day, while Jack is paid $1 more than the previous day.

On which day will they be paid the same amount of money?

$\{a_n\}$ is an arithmetic progression whose terms are $a_1, a_2, a_3, …$

$\{b_n\}$ is an arithmetic progression whose terms are $b_1, b_2, b_3, …$

If a new sequence $\{a_1 +b_1, a_2 + b_2, a_3 + b_3, …\}$ is made by adding the terms of $\{a_n\}$ and $\{b_n\}$, is the new sequence an arithmetic progression?

$\{a_n\}$ is an arithmetic progression whose terms are $a_1, a_2, a_3, ...$ and whose common difference is $d = a_2 - a_1.$

$\{b_n\}$ is an arithmetic progression created by multiplying each term in $\{a_n\}$ by 2.

$\{c_n\}$ is an arithmetic progression whose first term is the same as $\{a_n\}$ and whose common difference is twice the common difference of $\{a_n\}.$

What is the value of $b_{10} - c_{10}?$

Tom and Sarah start a new job. On Day 1, Tom is paid $20 and Sarah is paid $40. Each subsequent day, Tom is paid $5 more than the previous day, while Sarah is paid $3 more than the previous day.

At the end of Day 15, who has made a greater total amount of money over the course of the whole job?