Algebra

Arithmetic Progressions

Arithmetic Progression Comparisons

         

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?

{an}\{a_n\} is an arithmetic progression whose terms are a1,a2,a3,a_1, a_2, a_3, …

{bn}\{b_n\} is an arithmetic progression whose terms are b1,b2,b3,b_1, b_2, b_3, …

If a new sequence {a1+b1,a2+b2,a3+b3,}\{a_1 +b_1, a_2 + b_2, a_3 + b_3, …\} is made by adding the terms of {an}\{a_n\} and {bn}\{b_n\}, is the new sequence an arithmetic progression?

{an}\{a_n\} is an arithmetic progression whose terms are a1,a2,a3,...a_1, a_2, a_3, ... and whose common difference is d=a2a1.d = a_2 - a_1.

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

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

What is the value of b10c10?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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