1. Answer: 279,936
Step-by-step explanation:
The explicit rule for a geometric sequence is:
[tex]a_n=a_1(r)^{n-1}\qquad \text{where}\ a_1\ \text{is the first term and r is the common ratio}\\\\a_n=1(6)^{n-1}\qquad \rightarrow \quad a_1 = 1\ and\ r = 6\\\\a_8=1(6)^{8-1}\\\\.\quad=6^7\\\\.\quad=279,936[/tex]
2. Answer: -49,152
Step-by-step explanation:
The explicit rule for a geometric sequence is:
[tex]a_n=a_1(r)^{n-1}\qquad \text{where}\ a_1\ \text{is the first term and r is the common ratio}\\\\a_n=3(-4)^{n-1}\qquad \rightarrow \quad a_1 = 3\ and\ r = -4\\\\a_8=3(-4)^{8-1}\\\\.\quad=3(-4)^7\\\\.\quad=3(-16,384)\\\\.\quad=-49,152[/tex]
