Remember that finding terms in a geometric sequence is done by multiplying the previous term by a common ratio [tex]r[/tex]. For example, we can say:
[tex]a_2 = a_1 r[/tex]
[tex]a_3 = a_2 r = (a_1 r)r = a_1 r^2[/tex]
We have [tex]a_1 = 64[/tex]. To find [tex]a_2[/tex], let's multiply this term by [tex]\frac{5}{4}[/tex]:
[tex]a_2 = 64 \cdot \frac{5}{4} = 80[/tex]
Now, let's use this to find all of our other terms:
[tex]a_3 = 80 \cdot \frac{5}{4} = 100[/tex]
[tex]a_4 = 100 \cdot \frac{5}{4} = 125[/tex]
[tex]a_5 = 125 \cdot \frac{5}{4} = \frac{625}{4}[/tex]
Thus, our terms are 64, 80, 100, 125, and (625/4).