To solve this problem, we need to use the formula for the $n$th term of an arithmetic sequence:

$a_n = a_1 + (n-1) \cdot d$

Where:

• $a_n$ is the $n$th term,
• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Step 1: Set up equations using the information given.

You are given:

• The third term: $a_3 = -\frac{2}{3}$
• The eighth term: (a_8 = -\frac{22}{3