Question

Identify a pattern in the given list of numbers. Then use this pattern to find the next number.

Answer 1

Answer:

The given sequence is geometric sequence

In the given pattern we have next number is $a_5=\frac{1}{4}$

Step-by-step explanation:

Given numbers are 64,-16,4,-1

To identify the pattern of the given numbers :

Let $a_1=64$, $a_2=-16$ ,$a_3=4$  and $a_4=-1$

To find the next number that is $a_5$

common ratio $r=\frac{a_2}{a_1}$

$=\frac{-16}{64}$

$r=-\frac{1}{4}$

$r=\frac{a_3}{a_2}$

$=\frac{4}{-16}$

$r=-\frac{1}{4}$

Therefore the common ration is $r=-\frac{1}{4}$

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is $a_n=a_1r^{n-1}$

Now find the 5th term so put n=5 , $a_1=64andr=\frac{-1}{4}$ we have

$a_5=64(\frac{-1}{4})^{5-1}$

$=64(\frac{-1}{4})^{4}$

$=64(\frac{1}{4})^{4}$

$=64(\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4})$

$=\frac{1}{4}$

Therefore $a_5=\frac{1}{4}$