Question

Given the explicit formula for a geometric sequence find the common ratio and the 8th term.

1) an= 6n-1
2) an= 3• (-4) n-1

Answer 1

1. Answer: 279,936

Explanation:

The explicit rule for a geometric sequence is:

`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`

2. Answer: -49,152

Explanation:

The explicit rule for a geometric sequence is:

`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`