The explicit equation for the nth term of the geometric sequence 3584, 896, 224 is:
[tex]a_n=3584(0.25)^{n-1}\\\\\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]
Solution:
Given that we have to find the explicit equation for nth term of geometric sequence
Given sequence is:
3584, 896, 224
A geometric sequence has a common ratio
Let us find the common ratio. Divide each term by the previous term.
[tex]r=\frac{896}{3584} = 0.25\\\\r = \frac{224}{896} = 0.25[/tex]
Thus the common ratio is 0.25
The formula for nth term of geometric sequence is given as:
[tex]a_n=ar^{n-1}[/tex]
Where,
[tex]a_n[/tex] is the nth term of sequence
a is the first term of sequence
r is the common ratio
Here in given sequence 3584, 896, 224
first term = a = 3584
common ratio = r = 0.25
Therefore,
[tex]a_n=3584(0.25)^{n-1}[/tex]
[tex]\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]
"n" is a natural positive number greater than or equal to 1
Thus the explicit equation to find nth term is found
