Identify the Sequence 2 , 1 3/5 , 1 1/5

This is an arithmetic sequence since there is a common difference between each term. In this case, adding ${\displaystyle -\frac{2}{5}}$ to the previous term in the sequence gives the next term. In other words, ${\displaystyle a_n=a_1+d(n-1)}$.

Arithmetic Sequence: ${\displaystyle d=-\frac{2}{5}}$

This is the formula of an arithmetic sequence.

Substitute in the values of ${\displaystyle a_1=2}$ and ${\displaystyle d=-\frac{2}{5}}$.

To write ${\displaystyle 2}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{5}{5}}$.

Combine ${\displaystyle 2}$ and ${\displaystyle \frac{5}{5}}$.

Combine the numerators over the common denominator.