Answer:
[tex]b_n=-18\cdot 4^{n-1}[/tex]
Step-by-step explanation:
If the first term in a sequence is [tex]b_1=-18[/tex] and each term after the first is 4 times the preceding term, then the second term is
[tex]b_2=b_1\cdot 4=-18\cdot 4,[/tex]
the third term is
[tex]b_3=b_2\cdot 4=-18\cdot 4\cdot 4=-18\cdot 4^2,[/tex]
the fourth term is
[tex]b_4=b_3\cdot 4=-18\cdot 4^2\cdot 4=-18\cdot 4^3,[/tex]
...
the nth term is
[tex]b_n=b_{n-1}\cdot 4=...=b_1\cdot 4^{n-1}=-18\cdot 4^{n-1}[/tex]
