Answer:
see explanation
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
21 ÷ 7 = 63 ÷ 21 = 3
this indicates the sequence is geometric with explicit formula
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ration
here a₁ = 7 and r = 3 , then
[tex]a_{n}[/tex] = 7 . [tex]3^{n-1}[/tex] ← explicit formula
the recursive formula allows a term to be found by multiplying the previous term by r , then
[tex]a_{n}[/tex] = 7 . [tex]a_{n-1}[/tex] ← recursive formula
