Answer:
Equation: x(n)=2*4^(n-1)
a6=2048
Step-by-step explanation:
Take note that the common ratio is 4 because 2*4=8, 8*4=32, 32*4=128, and so on...
We will use the equation x(n) = ar^(n-1) where n represents the nth term, r stands for the common ratio, and "a" stands for the first term. We use (n-1) because ar^0 is for the 1st term
Given the first term is a=2, the common ratio is r=4, then we have the equation x(n)=2*4^(n-1)
So, 128*4=512 would be the 5th term, and the 6th term would be 512*4=2048
So a6=2048
We want to find an equation and the sixth term of the given geometric sequence.
The equation is:
[tex]A_n = 4*A_{n-1}[/tex]
And the sixth term is equal to 512
In a geometric sequence, each term is a constant times the previous term, so the general relation is:
[tex]A_n = k*A_{n-1}[/tex]
Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:
8 = k*2
8/2 = 4 = k
Now we know the value of the constant, then the general formula is:
[tex]A_n = 4*A_{n-1}[/tex]
Now we can use this to get the sixth term:
[tex]A_6 = 4*A_5 = 4*128 = 512[/tex]
If you want to learn more about geometric sequences, you can read:
https://brainly.com/question/9300199
