Find the 6th Term -1 , 2/3 , 7/3 , 4 , 17/3

This is an arithmetic sequence since there is a common difference between each term. In this case, adding ${\displaystyle \frac{5}{3}}$ to the previous term in the sequence gives the next term. In other words, ${\displaystyle a_n=a_1+d(n-1)}$.

Arithmetic Sequence: ${\displaystyle d=\frac{5}{3}}$

This is the formula of an arithmetic sequence.

Substitute in the values of ${\displaystyle a_1=-1}$ and ${\displaystyle d=\frac{5}{3}}$.

To write ${\displaystyle -1}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{3}{3}}$.

Combine ${\displaystyle -1}$ and ${\displaystyle \frac{3}{3}}$.

Combine the numerators over the common denominator.

Move the negative in front of the fraction.

Substitute in the value of ${\displaystyle n}$ to find the ${\displaystyle n}$th term.

Combine the numerators over the common denominator.