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