An arithmetic sequence is a sequence that starts with a given number and then increases (or decreases) by the same amount each term. For example:

starts with $5$ and then increases by $3$ each term. The starting number is usually labeled $a,$ so $a=5$ for the sequence above. The amount that gets added each term is usually labeled $d$ and is called the common difference.

So, an arithmetic sequence can be expressed as

We can see that

The $n^{\text{th}}$ term can either be given as an explicit formula

or a recursive formula

1. The arithmetic sequence $u_n$ begins

   $$200,194,182,176,\dots$$

   Find the ${20}^{\text{th}}$ term in this sequence.

2. The $5^{\text{th}}$ term of a different arithmetic sequence is $77.$

   The ${25}^{\text{th}}$ term is $-3.$

   Find the value of the ${14}^{\text{th}}$ term.