Write an equation for the nth term of the geometric sequence 2, 8, 32, 128, ... Then find a6. Round to the nearest tenth if necessary.

We want to find an equation and the sixth term of the given geometric sequence.

The equation is:

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:

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:

Now we can use this to get the sixth term:

If you want to learn more about geometric sequences, you can read:

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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

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step-by-step explanation:

yard and mile are too big.