[tex]a_{n+1} =7a_{n}[/tex].
If we know the term [tex]n^{th}[/tex] and the common relation, r, of a geometric sequence, you can find the term [tex](n+1)^{th}[/tex] using the recursive formula [tex]a_{n+1} =a_{n}.r[/tex].
The first term of the geometric sequence is a₁ = -3.
The common relation we have to find the relationship between a term and the term that precedes it.
[tex]r=\frac{-21}{-3} = 7[/tex]
The recursive formula is:
[tex]a_{1} =-3[/tex]
[tex]a_{n+1} =7a_{n}[/tex]
