[tex]a_{11}=a_{10}r[/tex]
[tex]a_{12}=a_{11}r=a_{10}r^2[/tex]
Since [tex]a_{10}=1[/tex], we have [tex]a_{12}=r^2=\dfrac1{25}[/tex], which means [tex]r=\pm\dfrac15[/tex].
Now,
[tex]a_2=a_1r[/tex]
[tex]a_3=a_2r=a_1r^2[/tex]
[tex]\cdots[/tex]
[tex]a_{10}=a_9r=\cdots=a_1r^9[/tex]
Since [tex]a_{10}=1[/tex] and [tex]r=\pm\dfrac15[/tex], we get
[tex]a_1=r^{-9}=\pm5^9[/tex]
