Certainly! Let's analyze the given pattern and predict the next three numbers:
The given sequence is: [tex]\( 25, 5, 1, \frac{1}{5}, \frac{1}{25} \)[/tex].
First, let's understand how the sequence progresses:
- The first term is [tex]\( 25 \)[/tex].
- The second term is [tex]\( 5 \)[/tex]. We see that [tex]\( 25 \div 5 = 5 \)[/tex].
- The third term is [tex]\( 1 \)[/tex]. We see that [tex]\( 5 \div 5 = 1 \)[/tex].
- The fourth term is [tex]\( \frac{1}{5} \)[/tex]. We see that [tex]\( 1 \div 5 = \frac{1}{5} \)[/tex].
- The fifth term is [tex]\( \frac{1}{25} \)[/tex]. We see that [tex]\( \frac{1}{5} \div 5 = \frac{1}{25} \)[/tex].
It appears that each term in the sequence is obtained by dividing the previous term by [tex]\( 5 \)[/tex].
Let's apply this pattern to find the next three terms:
1. For the sixth term:
[tex]\[
\frac{1}{25} \div 5 = \frac{1}{25 \times 5} = \frac{1}{125} = 0.008
\][/tex]
2. For the seventh term:
[tex]\[
0.008 \div 5 = \frac{0.008}{5} = 0.0016
\][/tex]
3. For the eighth term:
[tex]\[
0.0016 \div 5 = \frac{0.0016}{5} = 0.00032
\][/tex]
Therefore, the next three numbers in the pattern are:
[tex]\[ 0.008, 0.0016, 0.00032 \][/tex]
