The first few terms of a geometric sequence with first term [tex]a[/tex] and common ratio [tex]r[/tex] look like
[tex]a, ar , ar^2, ar^3, \ldots[/tex]
and so on. Notice that the [tex]n[/tex]-th term (where [tex]n[/tex] is a natural number) is [tex]ar^{n-1}[/tex].
For this particular sequence, the first term is
[tex]a=3[/tex]
and the fourth term is
[tex]ar^{4-1} = ar^3 = 1029[/tex]
Substitute [tex]a=3[/tex] into the second equation and solve for [tex]r[/tex].
[tex]3r^3 = 1029 \implies r^3 = 343 \implies r = \sqrt[3]{343} = \sqrt[3]{7^3} = 7[/tex]
Then the two terms between the 1st and 4th - i.e. the 2nd and 3rd terms - are
[tex]ar = 3\times7 = \boxed{21}[/tex]
and
[tex]ar^2 = 3\times7^2 = \boxed{147}[/tex]
