Answer: The next term in the given pattern is [tex]\dfrac{1}{4}.[/tex]
Step-by-step explanation: We are given to find the next number in the following pattern :
64, 16, 4, 1, . . .
We see that,
if a(n) denotes the nth number i the given pattern, then
a(1) = 64, a(2) = 16, a(3) = 4, a(4) = 1, . . .
That is,
[tex]\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.~~=\dfrac{1}{4}.[/tex]
Therefore, we get
[tex]\dfrac{a(5)}{a(4)}=\dfrac{1}{4}\\\\\\\Rightarrow \dfrac{a(5)}{1}=\dfrac{1}{4}\\\\\\\Rightarrow a(5)=\dfrac{1}{4}.[/tex]
Thus, the next term in the given pattern is [tex]\dfrac{1}{4}.[/tex]
