The common ratio between terms is 4/5, since
80/100 = 64/80 = 45
Since the sequence starts with [tex]a_1=100[/tex], we have
[tex]a_2 = \dfrac45 a_1[/tex]
[tex]a_2 = \dfrac45 a_1 = \left(\dfrac45\right)^2 a_1[/tex]
[tex]a_3 = \dfrac45 a_2 = \left(\dfrac45\right)^3 a_1[/tex]
and so on, up to the n-th term,
[tex]a_n = \left(\dfrac45\right)^n a_1[/tex]
Then the 12th term of the sequence is
[tex]a_{12} = \left(\dfrac45\right)^{12} \times 100 = \dfrac{2^{24}}{5^{12}} \times 2^2\times5^2 = \boxed{\dfrac{2^{26}}{5^{10}}} = \dfrac{67108864}{9765625}[/tex]
