Question

What is the 9th term of the geometric sequence where a1 = -8 and a6 = -8,192?

Answer 1

We must first find the common ratio `r`.

Explanation:

The `nth` term of a geometric series is given by `t_n = a xx r^(n - 1)`. We know `a`, the first term, we know `t_6`, and therefore we know `n (6)`

`-8192 = -8 xx r^(6 - 1)`

`-8192/-8 = r^5`

`1024 = r^5`

`root(5)(1024) = r`

`4 = r`

Now, we can reuse the formula `t_n = a xx r^(n - 1)` to find the 9th term.

`t_9 = -8 xx 4^(9 - 1)`

`t_9 = -8 xx 4^8`

`t_9 = -524288`

Therefore, `t_9` is -524 288.

Practice exercises:

1. Determine the 11th term of a geometric sequence where the first term is 27 and `t_4` is 1.

2. Determine the 7th term of a geometric sequence where the second term is 3 and the fifth is 375.

Hopefully this helps, and Good luck!