Question

Identify the 12th term of a geometric sequence where a1 = 8 and a6 = –8,192.

Answer 1

The nth term of a geometric sequence is found from the following formula:
`n _(th) \ term=a _(1) r^((n-1))`
Substituting the given values into the formula, we get:

`a _(6) =8r^(5)=-8192`

`r^(5)=-1028`
from which the common ratio r = -4.
Now we can use the value of r to find the required 12th term, as follows:

`a_(12) =8(-4)^(11)=-33,554,432`

Answer 2

The value of nth term is calculated by the equation,
an = (a1) x r^(n - 1)
Using this equation to find for the common ratio,
-8192 = 8 x r^(6 - 1)
The value or r is -4. Using the same equation to find for the 12th term,
a12 = 8 x (-4)^(12 - 1)
a12 = -33554432