Question

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).

Answer 1

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