In a theater, there are 20 seats in the first row. Each row...

In a theater, there are 20 seats in the first row. Each row has 3 more seats than the row ahead of it. There are 35 rows in the theater. a. Express the number of seats in the $n$ th row of the theater in terms of $n .$ b. Use sigma notation to represent the number of seats in the theater.

In a theater, there are 20 seats in the first row. Each row has 3 more seats than the row ahead of it. There are 35 rows in the theater.
a. Express the number of seats in the $n$ th row of the theater in terms of $n .$
b. Use sigma notation to represent the number of seats in the theater.

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Key Concepts

Arithmetic Series

An arithmetic series is the sum of the terms of an arithmetic sequence. It can be expressed and calculated in various ways, one common method being the use of the formula S? = n/2 × (a? + a?), where S? is the total sum, a? is the first term, a? is the n-th term, and n is the total number of terms.

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which each term after the first is generated by adding a constant difference to the previous term. The general formula for the n-th term of an arithmetic sequence is a? = a? + (n - 1)d, where a? represents the first term and d is the common difference between consecutive terms.

Sigma Notation

Sigma notation is a compact form of writing summations, using the sigma symbol (?) to indicate the sum of a sequence of terms. It includes specifying the starting index, the ending index, and a general expression for the terms being summed, providing a structured way to represent series mathematically.

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