Question

1/64, 1/16, 1/4, 1... What is the pattern and next term???

Answer 1

Answer:

$\huge\boxed{\text{next term}=4}\\\boxed{f(n)=4^{n-4}}$

Step-by-step explanation:

$\dfrac{1}{64},\ \dfrac{1}{16},\ \dfrac{1}{4},\ 1,\ ...$

It's the geometric sequence where

$a_1=\dfrac{1}{64},\ q=4$

$\dfrac{1}{16}=\dfrac{1}{64}\cdot4\\\\\dfrac{1}{4}=\dfrac{1}{16}\cdot4\\\\1=\dfrac{1}{4}\cdot4\\\\1\cdot4=4\to\text{next term}$

$f(n)=\dfrac{1}{64}\cdot4^{n-1}=\dfrac{1}{4^3}\cdot4^{n-1}=\dfrac{4^{n-1}}{4^3}\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\f(n)=4^{n-1-3}=4^{n-4}$