Question

Explicit equation for the nth term of the geometric sequence 3584,896,224,

Answer 1

The explicit equation for the nth term of the geometric sequence 3584, 896, 224 is:

$a_n=3584(0.25)^{n-1}\\\\\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}$

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.

$r=\frac{896}{3584} = 0.25\\\\r = \frac{224}{896} = 0.25$

Thus the common ratio is 0.25

The formula for nth term of geometric sequence is given as:

$a_n=ar^{n-1}$

Where,

$a_n$ 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,

$a_n=3584(0.25)^{n-1}$

$\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}$

"n" is a natural positive number greater than or equal to 1

Thus the explicit equation to find nth term is found