Given:
The sequence is:
12, 6, 3, ...
To find:
The formula for the nth term of the given sequence.
Solution:
We have,
12, 6, 3, ...
Here, first term is 12.
Clearly, [tex]\dfrac{6}{12}=\dfrac{3}{6}[/tex]. Since the given sequence has a common ratio [tex]r=dfrac{1}{2}[/tex], therefore it is a geometric sequence.
The formula for the nth term of the given sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
[tex]a_n=12\left(\dfrac{1}{2}\right)^{n-1}[/tex]
Therefore, the formula for the nth term of the given sequence is [tex]a_n=12\left(\dfrac{1}{2}\right)^{n-1}[/tex].
