Find the thirteenth term of a geometric sequence that has a first term of 4,096 and a common ratio of 1/2 (one-half).

1

Let's create a function for this geometric sequence. The general form of the function will be:

f (x) = C*R^x

where

C is some constant

R = ratio of sequential terms

x = term number.

We've been given 1/2 as the ratio. So we have:

f (x) = C*0.5^x

We've also been told that the first term is 4096. So we have

f (x) = C*0.5^x

4096 = C*0.5^1

Now let's solve for C

4096 = C*0.5^1

4096 = C*0.5

8192 = C

So our function is

f (x) = 8192*0.5^x

Let's solve for x = 13

f (x) = 8192*0.5^x

f (13) = 8192*0.5^13

f (13) = 8192*0.0001220703125

f (13) = 1