Given:
The sequence is
436, 218, 109, 54.5, 27.25,...
To find:
The explicit formula for the given sequence.
Solution:
We have,
436, 218, 109, 54.5, 27.25,...
It is a GP because the two consecutive terms have common ratio.
Here,
First term : a=436
Common ratio : d = [tex]\dfrac{218}{436}[/tex]
= [tex]\dfrac{1}{2}[/tex]
= [tex]0.5[/tex]
Now, the explicit formula for a GP is
[tex]g_n=ar^{(n-1)}[/tex]
Where, a is the first term and r is the common ratio.
Putting a=436 and r=0.5, we get
[tex]g_n=436(0.5)^{(n-1)}[/tex]
Therefore, the correct option is c.
