Question

What would be the next number in the pattern? 64, 16, 4, 1... A) 1/3 B) 1/5 C) 1/4 D) 1

Answer 1

Ur multiplying by 1/4 to get to the next number...so ur next number is 1/4

Answer 2

Answer:  The next term in the given pattern is $\dfrac{1}{4}.$

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,

$\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.~~=\dfrac{1}{4}.$

Therefore, we get

$\dfrac{a(5)}{a(4)}=\dfrac{1}{4}\\\\\\\Rightarrow \dfrac{a(5)}{1}=\dfrac{1}{4}\\\\\\\Rightarrow a(5)=\dfrac{1}{4}.$

Thus, the next term in the given pattern is $\dfrac{1}{4}.$