Dedicated to Mrs. Corricelli

Once, there was a 4th grader named Sally. Sally loved math and was always trying to apply what she learned in the classroom, to real life.

One day, Sally was helping her teacher set up for the school's math competition, and she came across a problem. She wanted to figure out how many seats were in the auditorium, but didn't have enough time to count every one.

How can I solve this problem?

Sally decided that in order to solve the problem she needed to first list the facts that she knew were true. She knew that there were sixteen total rows of seats. She also noticed that each row in the auditorium had one more seat than the last, and that the first row had seven seats. But what did this all mean?

After talking to her math teacher, Sally learned that in order to solve the problem, she must first learn what an arithmetic sequence is.

Arithmetic Sequences

An arithmetic sequence is an ordered list of numbers that have patterns that allow us to predict which number comes next by using math. Arithmetic sequences increase or decrease by the same amount each time, and can be modeled by the equation on the left.

Arithmetic Equation

In the equation, represents the first term of the sequence, which in this case, would be 7.

is the common difference of the series, or the increase or decrease between each term.

is the total number of terms, and is the final term of the sequence.

Now came the time for Sally to solve the first part of the equation and solve for . Since she knew the first row had 7 seats, that each row increased by 1, and that there were 16 total rows, she had her , , and v values.