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