The 9th term in this arithmetic sequence is [tex]\frac{13}{5}[/tex].
Step-by-step explanation:
We must first recall the formula for arithmetic sequence/progression.[tex]a_{n}=a_{1} +(n-1)d[/tex]
Distinguish all of the given terms in the formula, and find what is being asked.[tex]a_{9}=?[/tex][tex]n=9\\a_{1}=1\\d=\frac{1}{5}[/tex]
Substitute all of the given values in the formula above.[tex]a_{n}=a_{1} +(n-1)d\\a_{9}=1 +(9-1)\frac{1}{5}\\a_{9}=1 +(8)\frac{1}{5}\\a_{9}=1 +\frac{8}{5}\\a_{9}=\frac{5}{5} +\frac{8}{5}\\a_{9}=13/5[/tex]