Question

Identify the sequence as arithmetic or geometric, and write a recursive formula for the sequence. Be

sure to identify your starting value
The local football team won the championship several years ago, and since then, ticket prices have been increasing
$20 per year. The year they won the championship, tickets were $50. Write a recursive formula for a sequence
that models ticket prices. Is the sequence arithmetic or geometric?

Answer 1

Arithmetic Sequence

`a_(n) = 50 + (n-1) 20`

Explanation:

Since the increase in price for each year is a constant value we can safely say that this is an arithmetic sequence. Geometric sequences have changes that are based on multiples, i.e. prices double every year or half every year are multiples of 2 and 0.5 respectively

The general formula for any arithmetic sequence is as follow

`a_(n) = a_(1)  + (n - 1) d`

where

`a_(n)` = Ticket price at nth year

`a_(1)` = Starting ticket price (The year the team won the championship)

`n` = Number of years since the championship was won

`d` = Yearly increase in ticket price

So the formula can then be derived to be

`a_(n) = 50 + (n-1) 20`