Question

What is the 10th term of the sequence 64, 16, 4,...?

a. 1/1024

b. 1/256

c. 1/4096

d. 1/496

Answer 1

the answer is C. 1/4096

Answer 2

Each time we are dividing by 4.
Essentially, multiplying by 1/4.
Since we're multiplying, that makes this a geometric sequence!

So: Our first term is 64, and the common ratio is 1/4.
Let's plug that into the geometric sequence formula.


`a_n=a_1(r)^(n-1)`

Where a_n = the value of the nth term
a_1 = the first term, and r = the common ratio


`a_n=64(\frac14)^(n-1)`

Now that we have our equation, let's plug in 10 for n.
That way, we can solve to find
`a_(10)`, the value of the 10th term.


`a_(10)=64(\frac14)^(10-1)=\boxed{(1)/(4096)}`