Answer:
Step-by-step explanation:
Considering the geometric sequence
As the common ratio '
' between consecutive terms is constant.
The general term of a geometric sequence is given by the formula:
where 
is the initial term and the common ratio.
Putting 
, 
and in the general term of a geometric sequence to determine the 12th term of the sequence.
∵ 
Therefore,
4n² - 16n - 84 = 0
Multiply both sides by 1/4 :
n² - 4n - 21 = 0
Add 21 to both sides:
n² - 4n = 21
Complete the square by adding 4 to both sides:
n² - 4n + 4 = 25
(n - 2)² = 25
Solve for n :
n - 2 = ± √25
n - 2 = ± 5
n = 2 ± 5
Then n = 2 + 5 = 7 or n = 2 - 5 = -3.
