Question

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.

Answer 1

The equation for the nth term of the geometric sequence is a_n = 2 * 4^(n-1). The value of a6 is 2048.

Step-by-step explanation:

The formula for finding the nth term of a geometric sequence is:

a_n = a * r^(n-1)

where:

• a_n is the nth term
• a is the first term
• r is the common ratio

In this case, the first term (a) is 2 and the common ratio (r) is 4. So, the equation for the nth term is:

a_n = 2 * 4^(n-1)

To find a6, plug in n = 6:

a6 = 2 * 4^(6-1) = 2 * 4^5 = 2 * 1024 = 2048

Therefore, a6 is equal to 2048.

Answer 2

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