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# Arithmetic Progressions

What's the sum of the first 100 positive integers? How about the first 1000? Learn the fun and fast way to solve problems like this.

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?

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